Find derivatives of the functions defined as follows.y=4^(-5x+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
${\displaystyle f\left(t\right)=\frac{t^2-1}{t^2+t-2}}$

Find derivatives of the functions defined as follows.
${\displaystyle y=x{e}^x}$

Determine and simplify the first derivatives of the following functions.
${\displaystyle F\left(x\right)=\frac{1}{\sqrt{3}\left\{x\right\}}}$

Second derivatives Find ${\displaystyle \frac{d^{2}y}{{dx}^2}}$
${\displaystyle x+y=\sin y}$

Higher-Order Derivatives
${\displaystyle f\left(x\right)=2x^4-3x^3+2x^2+x+4}$
find ${\displaystyle f^{10}\left(x\right)=?}$