AP Calculus AB 2.8 Product Rule Question Bank

Practise product-rule questions by identifying factors, differentiating each factor and combining the terms.

5. Let f be the function whose graph is shown above; the graph of f consists of

three line segments.

Let g be a differentiable function. The table above gives values of g and its

derivative $g^{\prime}$ at various values of x.

(c) Let q be the function defined as $q(x)=f(-3 x) \cdot g(-2 x)$ . Find $q^{\prime}(-1)$ .

(c) $q^{\prime}(x)=-3 \cdot f^{\prime}(-3 x) \cdot g(-2 x)+f(-3 x) \cdot(-2) \cdot g^{\prime}(-2 x)$

$q^{\prime}(-1)=-3 \cdot f^{\prime}(3) \cdot g(2)+f(3) \cdot(-2) \cdot g^{\prime}(2)=(-3)(2)(3)$

+(2)(-2)(6)=-42

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FUN-3.B—Calculate derivatives of products and quotients of differentiable functions question 1