Derivative computed.
AskSia differentiates the function using the right rules, with each step labeled.
Derivative
EN
Tangent Line Solver
The tangent line at any point. Done.
Type or photograph the curve and the x-value or point. AskSia computes the derivative, evaluates it at your point to get the slope, plugs into point-slope form, simplifies, and graphs both the curve and the tangent line on the same axes.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How do you find the equation of a tangent line?
The tangent line at x = a on the curve y = f(x) has slope f'(a) and passes through (a, f(a)). Compute f'(x) using standard differentiation rules, evaluate at x = a to get the slope m. Plug into point-slope form: y - f(a) = m(x - a). Simplify to slope-intercept or another preferred form. The tangent line locally approximates the curve and is the basis of linearization and Newton's method.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Tangent Line.
Every step transparent, every answer self-checked.
Slope at the point.
f'(a) evaluated by substitution, with the arithmetic shown.
Slope
Point-slope to slope-intercept.
AskSia applies point-slope form and simplifies into y = mx + b or any requested form.
Form
Graph included.
Both the curve and the tangent line appear on the same axes, with the tangent point marked.
Visual
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Tangent Line problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Tangent Line solver covers.
Polynomial tangent.
Tangent to y = x^3 at x = 2. f'(2) = 12, apply point-slope.
Polynomial
Trig tangent.
Tangent to y = sin(x) at x = pi/4. Use f'(x) = cos(x).
Trig
Exponential tangent.
Tangent to y = e^x at x = 1. Use f'(x) = e^x.
Exponential
Implicit tangent.
For x^2 + y^2 = 25 at (3, 4), use implicit differentiation to find slope.
Implicit
Linearization.
L(x) = f(a) + f'(a)(x-a) approximates f near a.
Linearization
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
What is the geometric meaning of the tangent line?
The tangent line at a point on a curve is the line that just touches the curve at that point and has the same slope as the curve there. Geometrically, it is the limit of secant lines as the second point approaches the first. Algebraically, its slope is the derivative of the function at that point.
Can AskSia find the tangent line at a specific y-value?
Yes. If you give a point (x_0, y_0) that lies on the curve, AskSia computes the slope using f'(x_0). If you only give y_0, AskSia first solves f(x) = y_0 to find the x-values where the curve has that y-value (there may be multiple), then computes the tangent line at each.
How does the tangent line for an implicit equation differ?
For an implicit equation like x^2 + y^2 = 25, you cannot solve for y explicitly. Instead, use implicit differentiation: differentiate both sides with respect to x, treating y as a function of x, and solve for dy/dx. Evaluate at the given point to get the slope.
What is linearization?
Linearization uses the tangent line at x = a to approximate f(x) for x near a: L(x) = f(a) + f'(a)(x - a). For values of x close to a, L(x) is close to f(x), making it useful for quick approximations. AskSia provides L(x) alongside the tangent line equation.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Slope, point, line, graph.
Join 2M+ students using AskSia to solve tangent line problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.