6. Derivatives of Inverse, Exponential, & Logarithmic Functions

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.

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

Find the derivative of the given function.

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

Find the derivative of the given function.

$y=(4x-3x^2+9)\cdot2^{5x}$

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.

$f(x)=-3e^x+5x-2$

Find the derivative of the given function.

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

Find the derivative of the given function.

$y=x^2e^{3x^2+5x}$

Find the derivative of the given function.

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

Find the derivative of the given function.

$y=\tan \left(e^{-x^3}\right)$

Find the derivative of the given function.

$f(x)=8\log_2x$

Find the derivative of the given function.

$g(t)=2t+\log_5t$

Find the derivative of the given function.

$f(x)=(x^3+2x)\cdot\log_5x$

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.

$h\left(x\right)=\sin\left(\log_4\left(x^2\right)\right)$