Chain rule of differentiation Calculator

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 Example

 Solved Problems

 Difficult Problems

Here, we show you a step-by-step solved example of chain rule of differentiation. This solution was automatically generated by our smart calculator:

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

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

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

Add 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 $f'(x) = nx^{n-1}$

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

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 or more 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 is equal to the constant times the derivative of the function

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

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

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

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

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

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

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

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

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

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

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

Subtract the values $2$ and $-1$

$-4x$

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

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

Multiply $-2$ times $2$

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

 Final answer to the exercise

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

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 to the exercise

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