Solved example of quotient rule of differentiation
Apply the quotient rule for differentiation, which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
The derivative of the linear function is equal to $1$
Any expression multiplied by $1$ is equal to itself
The derivative of the linear function is equal to $1$
The derivative of a sum of two or more functions is the sum of the derivatives of each function
Simplify the product $-(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(1\right))$
The derivative of the constant function ($1$) is equal to zero
Multiply $-1$ times $0$
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 $f'(x) = nx^{n-1}$
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