6. Derivatives of Inverse, Exponential, & Logarithmic Functions

Identify the local minimum and maximum values of the given function, if any.

$f(t)=t^2\(\ln\) t$, $t>0$

For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.

Find the derivative of the given function.

$g(x)=e^{x}+\(\ln\) x^5$

Find the derivative of the given function.

$y=x^2\(\ln\)(x^2)$

Find the derivative of the given function.

$y=(4x-3x^2+9)\(\cdot\)2^{5x}$

Identify the open intervals on which the function is increasing or decreasing.

$f(x)=xe^{-2x}$

Find the derivative of the given function.

$g\(\left\)(t\(\right\))=\(\log\)_5\(\left\)(7^{t^2+4}\(\right\))$

Find the derivative of the given function.

$f(x)=2x^3-1+\(\ln\) x$

Find the derivative of the given function.

$f(x)=2^x-5^x$

Find the derivative of the given function.

$g(x)=x^4+4x+4^x$

Find the derivative of the given function.

$f(x)=(x^3+2x)\(\cdot\]\log\)_5x$

Find the derivative of the given function.

$g(x)=7e^x+2x^3$

Find the derivative of the given function.

$f(t)=\(\frac{e^{3t}\)}{t-2e^{-t}}$

Find the derivative of the given function.

$h\left(x\right)=4^{{(\sqrt{x}+3x)}^{\frac{5}{4}}}$

Find the derivative of the given function.

$h\(\left\)(x\(\right\))=\(\ln\]\left\)(\(\frac{\sqrt{x+1}\)}{x^2+3}\(\right\))$