Question:
If \( y = x^3 + \tan x \), then find \( \frac{d^2 y}{dx^2} \).
If \( y = x^3 + \tan x \), then find \( \frac{d^2 y}{dx^2} \).
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Use the chain rule when differentiating composite functions such as \( \tan x \).
Updated On: Mar 1, 2025
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Solution and Explanation
First derivative:
\[
\frac{dy}{dx} = 3x^2 + \sec^2 x.
\]
Second derivative:
\[
\frac{d^2y}{dx^2} = 6x + 2\sec^2 x \tan x.
\]
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