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# Product Rule of differentiation Calculator

## Get detailed solutions to your math problems with our Product 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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###  Difficult Problems

1

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

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

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=$\frac{d}{dx}\left(3x+2\right)\left(x^2-1\right)+\left(3x+2\right)\frac{d}{dx}\left(x^2-1\right)$3 The derivative of a sum of two or more functions is the sum of the derivatives of each function$\left(\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(2\right)\right)\left(x^2-1\right)+\left(3x+2\right)\frac{d}{dx}\left(x^2-1\right)$4 The derivative of a sum of two or more functions is the sum of the derivatives of each function$\left(\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(2\right)\right)\left(x^2-1\right)+\left(3x+2\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(-1\right)\right)$5 Apply the product rule for differentiation:$(f\cdot g)'=f'\cdot g+f\cdot g'$, where$f=

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

The derivative of the constant function ($3$) is equal to zero

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

The derivative of the constant function ($2$) is equal to zero

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

The derivative of the constant function ($-1$) is equal to zero

$\left(0+3\frac{d}{dx}\left(x\right)\right)\left(x^2-1\right)+\left(3x+2\right)\frac{d}{dx}\left(x^2\right)$
9

$x+0=x$, where $x$ is any expression

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

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

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

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

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

Subtract the values $2$ and $-1$

$2\left(3x+2\right)x$
11

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

$3\left(x^2-1\right)+2\left(3x+2\right)x$

Multiply the single term $3$ by each term of the polynomial $\left(x^2-1\right)$

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

Multiply $3$ times $-1$

$3x^2-3+2\left(3x+2\right)x$

Solve the product $2\left(3x+2\right)x$

$3x^2-3+\left(6x+4\right)x$

Multiply the single term $x$ by each term of the polynomial $\left(6x+4\right)$

$3x^2-3+6x\cdot x+4x$

When multiplying two powers that have the same base ($x$), you can add the exponents

$3x^2-3+6x^2+4x$

Combining like terms $3x^2$ and $6x^2$

$9x^2-3+4x$
12

Simplify the derivative

$9x^2-3+4x$

##  Final answer to the problem

$9x^2-3+4x$

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