Find derivatives for the functions. Assume a, b, c, and k are constants. y=17 x+24 x^{1 #x2F; 2}

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.

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

If f is a differentiable function, find an expression for the derivative of:
${\displaystyle y=\frac{2f\left(x\right)}{e^x}}$

Higher-order derivatives Find f′(x), f″(x), and f′″(x) for the following functions
${\displaystyle f\left(x\right)=3x^3+5x^2+6x}$

Find the four second partial derivatives of the following functions.
${\displaystyle f(x,y)=e^{2xy}}$

Find the derivative of $\tan (\frac{1}{4}\pi (2+x+6x^2+7x^3+4x^4))$.

Compute the derivatives, where c is a constant.
${\displaystyle \frac{d}{dt}c{t}^3}$