Define Higher order Derivatives ?

Question
Derivatives
Define Higher order Derivatives ?

2021-02-09
Step 1
To define: Higher Order Derivatives
Step 2
The first derivative of a function f(x) is another function f'(x)
The derivative of f'(x) is referred to as second order derivative f''(x)
This differentiation process can be continued to find the third, fourth, and successive derivatives of f( x), which are called higher order derivatives of f(x).
Example nth order derivative of f(x) will be $$\displaystyle{{f}^{{n}}{\left({x}\right)}}$$

Relevant Questions

Chain Rule and Higher Order Derivatives. Find the derivative
$$\displaystyle{f{{\left({x}\right)}}}={\left({5}{x}^{{{2}}}-{2}{x}+{1}\right)}^{{{3}}}$$
Find the following higher-order derivatives.
$$\displaystyle{\frac{{{d}^{{{n}}}}}{{{\left.{d}{x}\right.}^{{{n}}}}}}{\left({2}^{{{x}}}\right)}$$
Higher-order derivatives Find ƒ'(x), ƒ''(x), and ƒ'''(x) for the following functions.
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}-{7}{x}-{8}}}{{{x}+{1}}}}$$
Solve the higher order derivatives:
y''+6y=0
Solve the higher order derivatives:
y''-6y+9y=0, y(0)=2, y'(0)=0
Solve the higher order derivatives:
y''+4y+3y=0
$$\displaystyle{f}{''}{\left({x}\right)}={10}{x}^{{{3}}}-{32}{x}^{{{2}}}$$
$$\displaystyle{f{{\left({x},{y}\right)}}}={3}{x}^{{{7}}}{y}-{4}{x}{y}+{8}{y}$$
$$\displaystyle{{f}_{{\times}}{\left({x},{y}\right)}}=$$
$$\displaystyle{k}{\left({x},{y}\right)}={\frac{{-{7}{x}}}{{{2}{x}+{3}{y}}}}$$
Find all the second-order partial derivatives of the functions $$\displaystyle{g{{\left({x},{y}\right)}}}={{\cos{{x}}}^{{{2}}}-}{\sin{{3}}}{y}$$