Compute the derivative of the function $f(x) = x^2 + 3x + 5$.

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the derivative of the function $f(x) = x^2 + 3x + 5$, we need to apply the power rule and the sum rule. ‖ ‖ step 2 ⋮ The power rule states that the derivative of $x^n$ is $nx^{n-1}$. ‖ ‖ step 3 ⋮ Applying the power rule to $x^2$, we get $\frac{d}{dx}(x^2) = 2x$. ‖ ‖ step 4 ⋮ The derivative of $3x$ is $3$, and the derivative of the constant $5$ is $0$. ‖ ‖ step 5 ⋮ Adding these results together, we get $\frac{d}{dx}(x^2 + 3x + 5) = 2x + 3$. ‖ ∻Answer∻ ⚹ The derivative of the function $f(x) = x^2 + 3x + 5$ is $2x + 3$. ⚹ ∻Key Concept∻ ⚹Derivative⚹ ∻Explanation∻ ⚹The derivative of a function measures how the function's output value changes as the input value changes. In this case, we used the power rule and the sum rule to find the derivative of a polynomial function.⚹◊What is the general formula for calculating the derivative of a polynomial function?⍭ Generate me a similar question◊

Sia