Let g(x)=(1)/(x^(10)). g^(')(x)=

Identify Function: Identify the function to differentiate. We are given the function g(x) = 1/x^(10). We need to find its derivative, which is denoted by g^(')(x).Apply Power Rule: Apply the power rule for differentiation. The power rule states that the derivative of x^n with respect to x is n*x^(n-1). In this case, we can rewrite the function as g(x) = x^(-10) to apply the power rule.Differentiate Using Rule: Differentiate using the power rule. Taking the derivative of x^(-10) with respect to x gives us: g^(')(x) = -10 * x^(-10 - 1) g^(')(x) = -10 * x^(-11)Simplify Expression: Simplify the expression. The simplified form of the derivative is: g^(')(x) = -10/x^(11)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let $g(x)=\frac{1}{x^{10}}$ . $\newline$ $g^{\prime}(x)=$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Let

g(x)=\frac{1}{x^{10}}

\newline

g^{\prime}(x)=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $g(x) = \frac{1}{x^{10}}$ . We need to find its derivative, which is denoted by $g^{\prime}(x)$ .
Apply Power Rule: Apply the power rule for differentiation. $\newline$ The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ . In this case, we can rewrite the function as $g(x) = x^{-10}$ to apply the power rule.
Differentiate Using Rule: Differentiate using the power rule. $\newline$ Taking the derivative of $x^{-10}$ with respect to $x$ gives us: $\newline$ $g^{\prime}(x) = -10 \cdot x^{-10 - 1}$ $\newline$ $g^{\prime}(x) = -10 \cdot x^{-11}$
Simplify Expression: Simplify the expression. $\newline$ The simplified form of the derivative is: $\newline$ $g^{\prime}(x) = -\frac{10}{x^{11}}$