Understand Problem: We are asked to find the derivative of the function x^(-4) with respect to x. To do this, we will use the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).Apply Power Rule: Applying the power rule to x^(-4), we differentiate as follows: (d/dx)(x^(-4)) = -4 * x^(-4 - 1). We subtract 1 from the exponent of x.Simplify Expression: Simplify the expression: -4 * x^(-4 - 1) = -4 * x^(-5).Final Derivative: The final simplified form of the derivative is -4x^(-5). This is the answer to the problem.

Algebra 2

Simplify variable expressions using properties

Full solution

\frac{d}{d x}\left(x^{-4}\right)=

Understand Problem: We are asked to find the derivative of the function $x^{-4}$ with respect to $x$ . To do this, we will use the power rule for differentiation, which states that the derivative of $x^n$ with respect to $x$ is $n*x^{(n-1)}$ .
Apply Power Rule: Applying the power rule to $x^{-4}$ , we differentiate as follows: $(\frac{d}{dx})(x^{-4}) = -4 \cdot x^{-4 - 1}$ . We subtract $1$ from the exponent of $x$ .
Simplify Expression: Simplify the expression: $-4 \times x^{(-4 - 1)} = -4 \times x^{-5}.$
Final Derivative: The final simplified form of the derivative is $-4x^{-5}$ . This is the answer to the problem.