Chapter 29

Find the derivative. $$y=t^{2} \cos ^{-1} t$$

Find the derivative. $$y=7 \csc x^{3}$$

Integrate $$\int 7 \sec 3 \theta d \theta$$

Differentiate. $$y=\log \frac{(1+3 x)}{x^{2}}$$

Exponential Functions $$\int e^{2 x} d x$$

Find the rms value for each function in the given interval. \(y=\sin 2 x \quad\) from 0 to \(\pi / 2\).

Derivative of \(e^{u}\). Differentiate. $$y=e^{x^{2}}$$

First Derivatives Find the derivative. $$y=15.4 \cos ^{5} x$$

Find the derivative. $$y=9 \cot 3 x^{3}$$

Integrate $$\int x \sin x^{2} d x$$

Find the rms value for each function in the given interval. \(y=x+2 x^{2} \quad\) from 1 to 4.

Derivative of \(e^{u}\). Differentiate. $$y=e^{e^{x}}$$

First Derivatives Find the derivative. $$y=3.75 x \cos x$$

Find the derivative. $$y=\operatorname{Arctan}(1+2 x)$$

Find the derivative. $$y=x \tan x$$

Derivative of In \(u\) Differentiate. $$y=\ln x^{3}$$

Integrate $$\int 5 x \cos 2 x^{2} d x$$

Derivative of \(e^{u}\). Differentiate. $$y=e^{3 x^{2}+4}$$

First Derivatives Find the derivative. $$y=x^{2} \cos x^{2}$$

Find the derivative. $$y=\operatorname{Arccot}(2 x+5)^{2}$$

Find the derivative. $$y=x \sec x^{2}$$

Derivative of In \(u\) Differentiate. $$y=\ln \left(x^{2}-3 x\right)$$

Integrate $$\int \theta^{2} \tan \theta^{3} d \theta$$

Exponential Functions $$\int_{1}^{2} x e^{3 x^{2}} d x$$

Find the rms value for each function in the given interval. \(y=2 \cos x \quad\) from \(\pi / 6\) to \(\pi / 2\).

Derivative of \(e^{u}\). Differentiate. $$y=e^{\sqrt{1-x^{2}}}$$

First Derivatives Find the derivative. $$y=\sin ^{2}(\pi-x)$$

Find the derivative. $$y=\operatorname{Arccot} \frac{x}{a}$$

Find the derivative. $$y=5 x \csc 6 x$$

Derivative of In \(u\) Differentiate. $$y=\ln \left(4 x-x^{3}\right)$$

Exponential Functions $$\int_{3}^{4} \sqrt{e^{t}} d t$$

Find the rms value for each function in the given interval. \(y=5 \sin 2 x \quad\) from 0 to \(\pi / 6\).

Derivative of \(e^{u}\). Differentiate. $$y=x e^{x}$$

First Derivatives Find the derivative. $$y=\frac{\sin \theta}{\theta}$$

Find the derivative. $$y=\operatorname{Arcsec} \frac{1}{x}$$

Integrate $$\int \sin (x+1) d x$$

Derivative of \(e^{u}\). Differentiate. $$y=\frac{2}{e^{x}}$$

First Derivatives Find the derivative. $$y=\sin 2 \theta \cos \theta$$

Find the derivative. $$y=\operatorname{Arccsc} 2 x$$

Find the derivative. $$w=\sin \theta \tan 2 \theta$$

Derivative of In \(u\) Differentiate. $$w=z^{2} \ln \left(1-z^{2}\right)$$

Integrate $$\int \cos (7 x-3) d x$$

Derivative of \(e^{u}\). Differentiate. $$y=(3 x+2) e^{-x^{2}}$$

First Derivatives Find the derivative. $$y=\sin ^{5} \theta$$

Find the derivative. $$y=\operatorname{Arcsin} \sqrt{x}$$

Derivative of In \(u\) Differentiate. $$y=\frac{\ln (x+5)}{x^{2}}$$

Integrate $$\int \tan (4-5 \theta) d \theta$$

Exponential Functions $$\int_{0}^{1}\left(e^{x}-1\right)^{2} d x$$

Derivative of \(e^{u}\). Differentiate. $$y=x^{2} e^{3 x}$$

First Derivatives Find the derivative. $$y=\sin ^{2} x \cos x$$