Final Answer
Step-by-step Solution
Specify the solving method
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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
Simplify the product $-(x^5-x^4+x^2-2)$
Simplify the product $-(-x^4+x^2-2)$
Simplify the product $-(x^2-2)$
The derivative of a sum of two or more functions is the sum of the derivatives of each function
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
The derivative of the constant function ($1$) is equal to zero
The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
Simplify the derivative