Diketahui f(x)=√(x^3-8)

Diketahui $f(x)=\sqrt{x^3-8}$, maka $f^{\prime }(x)=\dots$

A. $\frac{3x^2}{2\sqrt{x^3-8}}$

B. $\frac{6x^2}{\sqrt{x^3-8}}$

C. $\frac{2}{\sqrt{x^3-8}}$

D. $\frac{3x}{2\sqrt{x^3-8}}$

E. $\frac{6x}{\sqrt{x^3-8}}$

Penyelesaian

$f(x)=\sqrt{x^3-8}\to f(x)=(x^3-8{)}^{\frac{1}{2}}$

$f^{\prime }(x)=\frac{1}{2}(x^3-8{)}^{\frac{1}{2}-1}(3x^2)$

$f^{\prime }(x)=\frac{1}{2}(x^3-8{)}^{-\frac{1}{2}}(3x^2)$

$f^{\prime }(X)=\frac{3x^2}{2(x^3-8{)}^{\frac{1}{2}}}$

$f^{\prime }(x)=\frac{3x^2}{2\sqrt{x^3-8}}$

Jawaban: A

Muda Berkarya Intelektual Normatif

Muda Berkarya Intelektual Normatif