Find the derivative of $g(x)=\frac{x^{3 / 2}-6 x+x^{1 / 2}}{x^{3 / 2}}$
with respect to x.
A) $\frac{3}{x^{3 / 2}}+\frac{-1}{x^{2}}$

B) $\frac{-48}{x^{3 / 2}}-\frac{-8.5}{x^{2}}$

C) $\frac{1.5 x^{05}-6+1 / 2 x^{-1 / 2}}{1.5 x^{0.5}}$

D)6x - 3

Question

Find the derivative of $g(x)=\frac{x^{3 / 2}-6 x+x^{1 / 2}}{x^{3 / 2}}$
 with respect to x.
A) $\frac{3}{x^{3 / 2}}+\frac{-1}{x^{2}}$

B) $\frac{-48}{x^{3 / 2}}-\frac{-8.5}{x^{2}}$

C) $\frac{1.5 x^{05}-6+1 / 2 x^{-1 / 2}}{1.5 x^{0.5}}$

D)6x - 3

Quizplus · Accepted Answer

First, simplify $g(x)$ to $1 - \frac{6}{x^{3/2}} + \frac{1}{x}$. Then, differentiate each term separately: the derivative of $1$ is $0$, the derivative of $-\frac{6}{x^{3/2}}$ is $9x^{-5/2}$, and the derivative of $\frac{1}{x}$ is $-x^{-2}$. Combine these to get $\frac{9}{x^{5/2}} - \frac{1}{x^2}$, which simplifies to $\frac{9x^{-3/2}}{x} - \frac{1}{x^2}$, matching none of the given options exactly due to a simplification error in the explanation. Correcting the process: the derivative of $-\frac{6}{x^{3/2}}$ is $\frac{9}{x^{5/2}}$, not $\frac{9}{x^{3/2}}$, indicating a mistake in the simplification process. The correct approach involves simplifying the original function and correctly applying the derivative rules, but the provided options and explanation indicate a misunderstanding or misapplication of these principles.

Find the Derivative Of g(x)=x3/2−6x+x1/2x3/2g(x)=\frac{x^{3 / 2}-6 x+x^{1 / 2}}{x^{3 / 2}}g(x)=x3/2x3/2−6x+x1/2​

Find the Derivative Of $g(x)=\frac{x^{3 / 2}-6 x+x^{1 / 2}}{x^{3 / 2}}$