Exam 33: Derivatives of Trigonometric, Logarithmic, and Exponential Functions

Differentiate implicitly: $x^{2}+y^{2}=x \ln y$

Find $\frac{d y}{d x}$ for $y=\ln (x \sec x)$ .

Find the derivative of $y=\frac{\tan x^{2}}{3}$ .

Find $\frac{d y}{d x}$ for the implicit function $x=\sin (y-x)$ .

Differentiate: $y=x^{2} e^{-x}$

Differentiate: $y=e^{x^{3}} \ln x^{2}$

Differentiate: $y=x^{\sin x}$

Find the second derivative of $y=4 \sin \left(2 x-\frac{\pi}{4}\right)$ .

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

Find the derivative of $y=\frac{x}{2} \tan^{-1} \frac{x}{2}$ .

Find the derivative: $r=\frac{\cot \theta}{\theta}$

Differentiate: $y=\ln \left(\sin \left(x^{2}+1\right)\right)$

Find the derivative: $y=\sin 3 x \cos 2 x$

Find $\frac{d y}{d x}$ for $2 e^{x y}=\ln x y-2$ .

Find the derivative of $y=\ln \left(2 x-\frac{3}{x}\right)$ .

Find the second derivative: $y=2 \tan 5 x$

Find $\frac{d y}{d x}$ for $y=\ln \left(x^{2} y\right)$ .

Find the maximum, minimum, and inflection points for $y=\frac{\ln x}{x^{2}}$ .

What is the maximum length of a board that you can fit around a $90^{\circ}$ corner if one hallway is $2.8 \mathrm{~m}$ wide and the other hallway is $1.4 \mathrm{~m}$ wide? (Round to 4 significant digits.)

Determine $\frac{d y}{d x}: 2 \ln y+\ln \left(x^{2}+4\right)=1$