6. Derivatives of Inverse, Exponential, & Logarithmic Functions

Find d/dx(ln√x²+1).

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.

$h\left(x\right)=4\left(\sqrt{x}+3x\right)^{\frac54}$

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.

$g\left(t\right)=\log_5\left(7^{t^2+4}\right)$