Chain Rule Practice Worksheet
A Grade 11 Calculus worksheet focusing on applying the Chain Rule for differentiation.
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Chain Rule Practice Worksheet
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Carefully read each question and apply the Chain Rule to find the derivative. Show all your work.
1. Find the derivative of $y = (3x^2 + 5x - 2)^4$.
2. Differentiate $f(x) = \sin(x^3)$.
3. Calculate the derivative of $g(x) = \sqrt{4x + 1}$.
4. If $y = \cos(u)$ and $u = x^2 + 3$, then $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = \underline{\hspace{40pt}} \cdot \underline{\hspace{40pt}} = \underline{\hspace{60pt}}$.
5. The Chain Rule is used to differentiate a function.
6. Which of the following is the derivative of $y = e^{2x}$?
$e^{2x}$
$2e^{2x}$
$e^2$
$2xe^{2x-1}$
7. The derivative of $y = (f(x))^n$ is $n(f(x))^{n-1} \cdot f'(x)$.
True
False
8. Find the derivative of $h(x) = \tan(e^{x^2})$.