Problem

if \( f(x)=\frac{1}{2 \sqrt{x}} \) then \( f^{\prime}(x)= \)
\( \sqrt{x} \)
not differentiable function
\( \frac{1}{4} \sqrt{x} \)
\( -\frac{1}{2} \sqrt{x} \)

Answer

Expert–verified

Hide Steps

Answer

\(f^{\prime}(x)= -\frac{1}{4} x^{-\frac{3}{2}}\)

Steps

Step 1 ：\(f(x)=\frac{1}{2\sqrt{x}}\)

Step 2 ：\(f^{\prime}(x)=\frac{d}{dx}\left(\frac{1}{2\sqrt{x}}\right)\)

Step 3 ：\(f^{\prime}(x)= -\frac{1}{4} x^{-\frac{3}{2}}\)

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More