AP Calculus AB: 2.8 The Product Rule – Exam Style questions with Answer- MCQ

Question

If \(y=x^{2}(e^{x}-1)\),then \(\frac{\mathrm{d} y}{\mathrm{d} x}\) is:

A \(2xe^{x}\)

B \(2xe^{x}-2x\)

C  \(x^{2}e^{x}+2xe^{x}-2x\)

D \(x^{2}e^{x}+2xe^{x}-x^{2}-2x\)

▶️Answer/Explanation

Ans:C

Question

The figure above shows the graphs of the functions f and g. If h(x) = f(x)g(x), then h'(2) =

A \(\frac{13}{2}\)

B \(\frac{1}{2}\)

C -1

D \(-\frac{11}{2}\)

▶️Answer/Explanation

Ans:D

Question

An equation of the line tangent to the graph of \(f(x)=x(1-2x)^{3}\) at the point (1,−1) is ,

A y=7x+6

B y=6x+5

C y=2x

D y=2x3

E y=7x−8

▶️Answer/Explanation

Ans:E

Question

If y=xsinx, then \(\frac{\mathrm{d} y}{\mathrm{d} x}\)=

A sinx+cosx

B sinx+xcosx

C sinxxcosx

D x(sinx+cosx)

E x(sinxcosx)

▶️Answer/Explanation

Ans:B

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