Find \frac{\partical f}{\partical x}, \frac{\partical f}{\partical y} and \frac{\partical f}{\partical z} for the function f(x,y,z)=x^{2}y+y^{2}+xz^{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 following derivatives.
${\displaystyle \ln \left(\frac{x+3}{x^2}\right)}$

Find all first and the second partial derivatives.
${\displaystyle f(x,y)=2x^5{y}^2+x^{2}y}$

Find the derivatives.
${\displaystyle f\left(x\right)=\frac{4x^3+\sqrt[3]{x}-6x}{x^{\frac{1}{2}}}}$

Use derivatives to find the critical points and inflection points. ${\displaystyle f\left(x\right)=x^3-9x^2+24x+5}$

Second derivatives Find ${\displaystyle d^2\frac{y}{{dx}^2}}$ for the following functions. ${\displaystyle y=2x^2+2}$