Solved example of product rule of differentiation
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=3x+2$ and $g=x^2-1$
The derivative of a sum of two or more functions is the sum of the derivatives of each function
The derivative of the constant function ($2$) is equal to zero
$x+0=x$, where $x$ is any expression
The derivative of the constant function ($2$) is equal to zero
The derivative of a function multiplied by a constant ($3$) is equal to the constant times the derivative of the function
The derivative of the linear function is equal to $1$
The derivative of the linear function times a constant, is equal to the constant
The derivative of a sum of two or more functions is the sum of the derivatives of each function
The derivative of the constant function ($2$) is equal to zero
$x+0=x$, where $x$ is any expression
$x+0=x$, where $x$ is any expression
The derivative of the constant function ($-1$) is equal to zero
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
Subtract the values $2$ and $-1$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
Multiply the single term $3$ by each term of the polynomial $\left(x^2-1\right)$
Multiply $-1$ times $3$
Solve the product $2x\left(3x+2\right)$
Multiply the single term $x$ by each term of the polynomial $\left(2\cdot 3x+2\cdot 2\right)$
Multiply $2$ times $3$
When multiplying two powers that have the same base ($x$), you can add the exponents
Multiply $2$ times $2$
Combining like terms $3x^2$ and $6x^2$
Simplifying
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