derivative of 1/((1-2x^{3/2)})

해법

\frac{d}{d x} (\frac{1}{( 1 - 2 x ) ^{\frac{3}{2}}})

\frac{3}{( 1 - 2 x ) ^{\frac{5}{2}}}

솔루션 단계

\frac{d}{d x} (\frac{1}{( 1 - 2 x ) ^{\frac{3}{2}}})

지수 규칙 적용:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((1 - 2 x)^{- \frac{3}{2}})

체인 규칙 적용:

- \frac{3}{2 ( 1 - 2 x ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - 2 x)

= - \frac{3}{2 ( 1 - 2 x ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - 2 x)

\frac{d}{d x} (1 - 2 x) = - 2

= - \frac{3}{2 ( 1 - 2 x ) ^{\frac{5}{2}}} (- 2)

- \frac{3}{2 ( 1 - 2 x ) ^{\frac{5}{2}}} (- 2)

간소화하다 :

\frac{3}{( 1 - 2 x ) ^{\frac{5}{2}}}

= \frac{3}{( 1 - 2 x ) ^{\frac{5}{2}}}