Let g(x)=ln(x^(4)). Find g^(')(x). Choose 1 answer: (A) (4)/(x) (B) (1)/(x^(4)) (C) 4ln(x^(3)) (D) (1)/(ln(x))+4x^(3)

Apply Chain Rule: Apply the chain rule to differentiate g(x) = ln(x^(4)). The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. Here, the outer function is ln(u) and the inner function is u = x^(4). The derivative of ln(u) with respect to u is 1/u, and the derivative of u = x^(4) with respect to x is 4x^(3). So, g'(x) = (1/u) * (du/dx) = (1/x^(4)) * (4x^(3)).Simplify Expression: Simplify the expression for g'(x). We have g'(x) = (1/x^(4)) * (4x^(3)). When we multiply the fractions, we can cancel out x^(3) from the numerator and denominator. This gives us g'(x) = 4/x.Match Answer Choices: Match the simplified expression to the given answer choices. The simplified expression for the derivative is g'(x) = 4/x, which corresponds to answer choice (A) (4)/(x).

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Let
g(x)=ln(x^(4)).
Find
g^(')(x).
Choose 1 answer:
(A)
(4)/(x)
(B)
(1)/(x^(4))
(C)
4ln(x^(3))
(D)
(1)/(ln(x))+4x^(3)

Let $g(x)=\ln \left(x^{4}\right)$ . $\newline$ Find $g^{\prime}(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{4}{x}$ $\newline$ (B) $\frac{1}{x^{4}}$ $\newline$ (C) $4 \ln \left(x^{3}\right)$ $\newline$ (D) $\frac{1}{\ln (x)}+4 x^{3}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Let

g(x)=\ln \left(x^{4}\right)

\newline

Find

g^{\prime}(x)

\newline

Choose

1

answer:

\newline

(A)

\frac{4}{x}

\newline

(B)

\frac{1}{x^{4}}

\newline

(C)

4 \ln \left(x^{3}\right)

\newline

(D)

\frac{1}{\ln (x)}+4 x^{3}

Apply Chain Rule: Apply the chain rule to differentiate $g(x) = \ln(x^{4})$ . The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. Here, the outer function is $\ln(u)$ and the inner function is $u = x^{4}$ . The derivative of $\ln(u)$ with respect to $u$ is $\frac{1}{u}$ , and the derivative of $u = x^{4}$ with respect to $x$ is $4x^{3}$ . So, g'(x) = \left(\frac{$1$}{u}\right) \cdot \left(\frac{du}{dx}\right) = \left(\frac{$1$}{x^{$4$}}\right) \cdot \left(\(4x^{ $3$ }\right)\.
Simplify Expression: Simplify the expression for $g'(x)$ . We have $g'(x) = \frac{1}{x^{4}} \cdot (4x^{3})$ . When we multiply the fractions, we can cancel out $x^{3}$ from the numerator and denominator. This gives us $g'(x) = \frac{4}{x}$ .
Match Answer Choices: Match the simplified expression to the given answer choices. $\newline$ The simplified expression for the derivative is $g'(x) = \frac{4}{x}$ , which corresponds to answer choice (A) $\frac{4}{x}$ .