What is the derivative of 1/((1-x^6^{3/2)}) ?

The derivative of 1/((1-x^6^{3/2)}) is (9x^5)/((1-x^6)^{5/2)}

What is the first derivative of 1/((1-x^6^{3/2)}) ?

The first derivative of 1/((1-x^6^{3/2)}) is (9x^5)/((1-x^6)^{5/2)}

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\frac{d}{d x} (\frac{1}{( 1 - x ^{6} ) ^{\frac{3}{2}}})

\frac{9 x ^{5}}{( 1 - x ^{6} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{( 1 - x ^{6} ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= \frac{d}{d x} ((1 - x^{6})^{- \frac{3}{2}})

Apply the chain rule:

- \frac{3}{2 ( 1 - x ^{6} ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - x^{6})

= - \frac{3}{2 ( 1 - x ^{6} ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - x^{6})

\frac{d}{d x} (1 - x^{6}) = - 6 x^{5}

= - \frac{3}{2 ( 1 - x ^{6} ) ^{\frac{5}{2}}} (- 6 x^{5})

Simplify

- \frac{3}{2 ( 1 - x ^{6} ) ^{\frac{5}{2}}} (- 6 x^{5}) : \frac{9 x ^{5}}{( 1 - x ^{6} ) ^{\frac{5}{2}}}

= \frac{9 x ^{5}}{( 1 - x ^{6} ) ^{\frac{5}{2}}}

\int_{0}^{N} e^{- s t} e^{- 3 t} d t

y^{^{'}} - (4 x - y + 1)^{2} = 0

\frac{d}{d x} (\frac{1}{0})

\int sin (2) d x

\frac{d y}{d x} + \frac{3 y}{x} + 2 = 3 x

What is the derivative of 1/((1-x^6^{3/2)}) ?
The derivative of 1/((1-x^6^{3/2)}) is (9x^5)/((1-x^6)^{5/2)}
What is the first derivative of 1/((1-x^6^{3/2)}) ?
The first derivative of 1/((1-x^6^{3/2)}) is (9x^5)/((1-x^6)^{5/2)}