Find derivatives of the functions defined as follows.y=3*4^(x^2+2)

Use the given graph to estimate the value of each derivative.(Round all answers to one decimal place.)Graph uploaded below.
(a) f ' (0)1
(b) f ' (1)2
(c) f ' (2)3
(d) f ' (3)4
(e) f ' (4)5
(f) f ' (5)6

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders? Give examples.

Find the derivatives of the functions ${\displaystyle y={(3+{\cos }^{3}3x)}^{-\frac{1}{3}}}$

Find the derivatives of ${\displaystyle x={\sin h}^{2}y}$

What is the derivative of $$\frac{\tan (\pi x)}{\ln (x)}$$?

Find the derivatives of the functions. ${\displaystyle r\left(x\right)=\ln |x+e^x|}$

Find the higher order derivatives for ${\displaystyle f\left(x\right)=x^5}$, what is ${\displaystyle f^6\left(x\right)}$?