Let g(x)=-(5)/(x). Find g^('')(x). g^('')(x)=

Find Derivative of g(x): Find the first derivative of g(x). To find the first derivative of g(x) = -(5/x), we use the power rule for derivatives. The function can be rewritten as g(x) = -5x^(-1). Differentiating -5x^(-1) with respect to x gives us g'(x) = 5x^(-2).Simplify First Derivative: Simplify the first derivative. The first derivative simplifies to g'(x) = 5/x^2.Find Second Derivative: Find the second derivative of g(x). Now we need to differentiate g'(x) = 5/x^2 to find the second derivative. This can be rewritten as g'(x) = 5x^(-2). Differentiating 5x^(-2) with respect to x gives us g''(x) = -10x^(-3).Simplify Second Derivative: Simplify the second derivative. The second derivative simplifies to g''(x) = -10/x^3.

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Let
g(x)=-(5)/(x).
Find
g^('')(x).

g^('')(x)=

Let $g(x)=-\frac{5}{x}$ . $\newline$ Find $g^{\prime \prime}(x)$ . $\newline$ $g^{\prime \prime}(x)=$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Let

g(x)=-\frac{5}{x}

\newline

Find

g^{\prime \prime}(x)

\newline

g^{\prime \prime}(x)=

Find Derivative of $g(x)$ : Find the first derivative of $g(x)$ . To find the first derivative of $g(x) = -(\frac{5}{x})$ , we use the power rule for derivatives. The function can be rewritten as $g(x) = -5x^{-1}$ . Differentiating $-5x^{-1}$ with respect to $x$ gives us $g'(x) = 5x^{-2}$ .
Simplify First Derivative: Simplify the first derivative. $\newline$ The first derivative simplifies to $g'(x) = \frac{5}{x^2}$ .
Find Second Derivative: Find the second derivative of $g(x)$ . $\newline$ Now we need to differentiate $g'(x) = \frac{5}{x^2}$ to find the second derivative. This can be rewritten as $g'(x) = 5x^{-2}$ . $\newline$ Differentiating $5x^{-2}$ with respect to $x$ gives us $g''(x) = -10x^{-3}$ .
Simplify Second Derivative: Simplify the second derivative. $\newline$ The second derivative simplifies to $g''(x) = -\frac{10}{x^3}$ .