Chain rule for y.
Every y term picks up a dy/dx factor when differentiated, with AskSia tracking each occurrence.
Chain rule
AI Solver by AskSia
Implicit Differentiation Solver: dy/dx for any equation
Type or photograph the implicit equation. AskSia differentiates both sides with respect to x, applies the chain rule to terms containing y (multiplying by dy/dx), and solves the resulting linear equation in dy/dx. The answer comes in terms of x and y.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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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 does implicit differentiation work?
When y is defined implicitly by an equation in x and y (like x^2 + y^2 = 25), you cannot always solve for y explicitly. Instead, differentiate both sides with respect to x, treating y as a function of x. Each y term gets the chain rule: differentiating y^n gives n*y^(n-1) * dy/dx. After differentiating, the result is a linear equation in dy/dx; solve it to express dy/dx as a function of x and y.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Implicit Differentiation.
Every step transparent, every answer self-checked.
Linear in dy/dx.
After differentiation, the result is linear in dy/dx. AskSia collects terms and isolates dy/dx.
Algebraic
Answer in x and y.
dy/dx is expressed in terms of both variables, since y is not solvable as an explicit function of x.
Implicit form
Higher-order on request.
Second derivative d^2y/dx^2 by differentiating dy/dx implicitly, with dy/dx substituted back in.
Higher-order
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 Implicit Differentiation 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
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Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
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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
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Implicit Differentiation solver covers.
Circle.
x^2 + y^2 = 25. dy/dx = -x/y. AskSia derives and simplifies.
Conic
Curve in two variables.
x^3 + y^3 = 3xy (folium). AskSia handles the algebra.
Curve
Tangent lines to implicit curves.
Find tangent to x^2 + xy + y^2 = 7 at (1, 2). AskSia computes slope.
Tangent
Related rates.
For two related quantities, differentiate implicitly with respect to time.
Related rates
Inverse function derivatives.
If y = arcsin(x), use sin(y) = x and implicit differentiation.
Inverse
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.
Why do I need implicit differentiation?
Because many curves cannot be expressed as y = f(x) explicitly. The circle x^2 + y^2 = 25 has two branches, so y is not a single function of x. Implicit differentiation lets you find dy/dx anywhere on the curve without committing to one branch.
How is the chain rule applied to y terms?
When differentiating an expression containing y with respect to x, treat y as a function of x. The chain rule says d/dx of y^n equals n*y^(n-1) * dy/dx. For more complex expressions like sin(y), the derivative is cos(y) * dy/dx. The dy/dx factor appears every time y is differentiated.
What does the final dy/dx in terms of x and y mean?
The slope of the tangent line at any point (x, y) on the curve depends on both coordinates. For x^2 + y^2 = 25, dy/dx = -x/y, so the slope at (3, 4) is -3/4 and at (3, -4) is 3/4. The same formula handles both branches because y carries the branch information.
Can implicit differentiation give the second derivative?
Yes. After finding dy/dx implicitly, differentiate it again with respect to x (using the quotient rule if needed) to get d^2y/dx^2. The result will contain dy/dx, which you replace by its expression from the first calculation.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. 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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Differentiate, isolate dy/dx, simplify.
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