Higher-order derivatives Calculator

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1

Example

$\frac{d^2}{dx^2}\left(\left(x-1\right)^3\right)\left(x-3\right)$
2

Rewriting the high order derivative

$\left(x-3\right)\frac{d^{\left(2-1\right)}}{dx^{\left(2-1\right)}}\left(\frac{d}{dx}\left(\left(x-1\right)^3\right)\right)$
3

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\left(x-3\right)\frac{d^{\left(2-1\right)}}{dx^{\left(2-1\right)}}\left(3\left(x-1\right)^{2}\cdot\frac{d}{dx}\left(x-1\right)\right)$
4

The derivative of a sum of two functions is the sum of the derivatives of each function

$\left(x-3\right)\frac{d^{\left(2-1\right)}}{dx^{\left(2-1\right)}}\left(3\left(x-1\right)^{2}\left(\frac{d}{dx}\left(-1\right)+\frac{d}{dx}\left(x\right)\right)\right)$
5

The derivative of the constant function is equal to zero

$\left(x-3\right)\frac{d^{\left(2-1\right)}}{dx^{\left(2-1\right)}}\left(3\left(x-1\right)^{2}\left(0+\frac{d}{dx}\left(x\right)\right)\right)$
6

The derivative of the linear function is equal to $1$

$\left(x-3\right)\frac{d^{\left(2-1\right)}}{dx^{\left(2-1\right)}}\left(\left(0+1\right)\cdot 3\left(x-1\right)^{2}\right)$
7

Subtract the values $2$ and $-1$

$\left(x-3\right)\frac{d^{1}}{dx^{1}}\left(\left(0+1\right)\cdot 3\left(x-1\right)^{2}\right)$
8

Add the values $1$ and $0$

$\left(x-3\right)\frac{d^{1}}{dx^{1}}\left(1\cdot 3\left(x-1\right)^{2}\right)$
9

Multiply $3$ times $1$

$\left(x-3\right)\frac{d^{1}}{dx^{1}}\left(3\left(x-1\right)^{2}\right)$
10

Any expression to the power of $1$ is equal to that same expression

$\left(x-3\right)\frac{d}{dx}\left(3\left(x-1\right)^{2}\right)$
11

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$3\left(x-3\right)\frac{d}{dx}\left(\left(x-1\right)^{2}\right)$
12

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$3\cdot 2\left(x-3\right)\left(x-1\right)\frac{d}{dx}\left(x-1\right)$
13

The derivative of a sum of two functions is the sum of the derivatives of each function

$3\cdot 2\left(x-3\right)\left(x-1\right)\left(\frac{d}{dx}\left(-1\right)+\frac{d}{dx}\left(x\right)\right)$
14

The derivative of the constant function is equal to zero

$3\cdot 2\left(x-3\right)\left(x-1\right)\left(0+\frac{d}{dx}\left(x\right)\right)$
15

The derivative of the linear function is equal to $1$

$3\cdot \left(0+1\right)\cdot 2\left(x-3\right)\left(x-1\right)$
16

Add the values $1$ and $0$

$3\cdot 1\cdot 2\left(x-3\right)\left(x-1\right)$
17

Multiply $3$ times $2$

$6\left(x-3\right)\left(x-1\right)$