Question

Find \(\mathrm{dy} / \mathrm{dt}\).

12) \(y=\cos ^{5}(\pi t-8)\)

A) \(-5 \pi \cos ^{4}(\pi t-8) \sin (\pi t-8)\)

B) \(-5 \cos ^{4}(\pi \mathrm{t}-8) \sin (\pi \mathrm{t}-8)\)

C) \(5 \cos ^{4}(\pi t-8)\)

D) \(-5 \pi \sin ^{4}(\pi t-8)\)

Use implicit differentiation to find dy/dx.

13) \(x y+x=2\)

A) \(-\frac{1+y}{x}\)

B) \(\frac{1+y}{x}\)

C) \(\frac{1+x}{y}\)

D) \(-\frac{1+x}{y}\)

Find the derivative of \(y\) with respect to \(x, t\), or \(\theta\), as appropriate.

14) \(y=\ln 8 x^{2}\)

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

B) \(\frac{1}{2 x+8}\)

C) \(\frac{2 x}{x^{2}+8}\)

D) \(\frac{16}{x}\)

Find the derivative of \(\mathrm{y}\) with respect to \(\mathrm{x}, \mathrm{t}\), or \(\theta\), as appropriate.

15) \(y=\left(x^{2}-2 x+6\right) e^{x}\)

A) \(\left(x^{2}+4 x+4\right) e^{x}\)

B) \(\left(x^{2}+4\right) e^{x}\)

C) \(\left(\frac{x^{3}}{3}+4 x+6\right) \mathrm{e}^{\mathrm{x}}\)

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

Find the derivative of \(y\) with respect to \(x\).

16) \(y=3 \sin ^{-1}\left(5 x^{4}\right)\)

A) \(\frac{3}{\sqrt{1-25 x^{8}}}\)

B) \(\frac{60 x^{3}}{\sqrt{1-25 x^{8}}}\)

C) \(\frac{60 x^{3}}{1-25 x^{8}}\)

D) \(\frac{60 x^{3}}{\sqrt{1-25 x^{4}}}\)

Answer 1