Chain rule of differentiation Calculator

Get detailed solutions to your math problems with our Chain rule of differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

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Example

Solved Problems

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Solved example of chain rule of differentiation

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

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

Subtract the values $3$ and $-1$

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

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

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

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 $1$

$3$

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

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

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

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

$3\left(3x-2x^2\right)^{2}\left(3-2\cdot 2x^{\left(2-1\right)}\right)$

Subtract the values $2$ and $-1$

$3\left(3x-2x^2\right)^{2}\left(3-2\cdot 2x^{1}\right)$

Multiply $-2$ times $2$

$3\left(3x-2x^2\right)^{2}\left(3-4x^{1}\right)$

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

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

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

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

Chain rule of differentiation Calculator

Get detailed solutions to your math problems with our Chain rule of differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

Example

Solved Problems

Difficult Problems

Final Answer

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