Question 1
1 markFind the derivative \( \frac{dy}{dx} \) for the function \( y = \cos(e^x) \).
AP (Advanced Placement) · AP Calculus AB
The chain rule: Practice Questions
5 multiple-choice questions marked as you go, and 1 written questions with worked solutions. All on The chain rule.
6 questions9 marksFree, no account
Question 2
1 markConsider the function \( f(x) = \sin^{-1}(2x) \). Find the value of \( f''(x) \) at \( x = \frac{1}{4} \).
Question 3
1 markLet \( f(x) = x^3 + x \). Let \( g(x) = f^{-1}(x) \) be the inverse function of \( f \). Find the value of \( g'(2) \).
Question 4
1 markFind the derivative of the composite function \( f(x) = (3x^2 + 2)^5 \) with respect to \( x \).
Question 5
1 markGiven the equation \( x^2 + y^2 = 25 \), find the slope of the tangent line at the point \( (3, 4) \) using implicit differentiation.
Question 6
4 marksA curve is defined by the implicit equation \( x^2 + 2xy - y^3 = 7 \). Determine the equation of the tangent line to the curve at the point \( (3, 2) \).
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