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Chain rule of differentiation Calculator

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1

Solved example of chain rule of differentiation

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

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

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

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

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

The derivative of a function multiplied by a constant ($3$) is equal to the constant times the derivative of the function

$3\frac{d}{dx}\left(x\right)$

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

$3$
4

The derivative of the linear function times a constant, is equal to the constant

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

The derivative of a function multiplied by a constant ($-2$) is equal to the constant times the derivative of the function

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

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

$3\left(3x-2x^2\right)^{2}\left(3-4x\right)$

Final Answer

$3\left(3x-2x^2\right)^{2}\left(3-4x\right)$

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