Let $g(x)=-4 \log _{3}(x)$.
Find $g^{\prime}(x)$.
Choose 1 answer:
(A) $-\frac{4}{x \ln (3)}$
(B) $-\frac{4 \ln (x)}{\ln (3)}$
(C) $-\frac{4}{x \log _{3}(x)}$
(D) $-\frac{4}{x}$

Question

Let $g(x)=-4 \log _{3}(x)$.
Find $g^{\prime}(x)$.
Choose 1 answer:
(A) $-\frac{4}{x \ln (3)}$
(B) $-\frac{4 \ln (x)}{\ln (3)}$
(C) $-\frac{4}{x \log _{3}(x)}$
(D) $-\frac{4}{x}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the derivative of $g(x)=-4\log_3(x)$, we apply the chain rule and the logarithmic differentiation formula $\frac{d}{dx}(\log_a(x)) = \frac{1}{x\ln(a)}$ where $a$ is the base of the logarithm. ‖ ‖ step 2 ⋮ Applying the formula to $g(x)$, we get $g'(x) = \frac{d}{dx}(-4\log_3(x)) = -4 \cdot \frac{1}{x\ln(3)}$. ‖ ‖ step 3 ⋮ Simplifying the expression, we have $g'(x) = -\frac{4}{x\ln(3)}$. ‖ ***A*** ∻Key Concept∻ ⚹Derivative of a logarithmic function⚹ ∻Explanation∻ ⚹The derivative of $\log_a(x)$ with respect to $x$ is $\frac{1}{x\ln(a)}$, where $a$ is the base of the logarithm. When multiplied by a constant, the constant is factored out as part of the derivative.⚹◊What is the derivative of the function $g(x) = -4 \log_{3}(x)$?⍭ Generate me a similar question◊

Sia