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

The derivative of 6/((6-x^6)^{3/2)} is (54x^5)/((6-x^6)^{5/2)}

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

The first derivative of 6/((6-x^6)^{3/2)} is (54x^5)/((6-x^6)^{5/2)}

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derivative of

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

\frac{54 x ^{5}}{( 6 - x ^{6} ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

6 (- \frac{3}{2 ( 6 - x ^{6} ) ^{\frac{5}{2}}} (- 6 x^{5})) : \frac{54 x ^{5}}{( 6 - x ^{6} ) ^{\frac{5}{2}}}

= \frac{54 x ^{5}}{( 6 - x ^{6} ) ^{\frac{5}{2}}}

\int \frac{x ^{3}}{( x ^{2} + 4 ) ^{\frac{3}{2}}} d x

\frac{6}{( s + 3 ) ^{2}}

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

x^{2}

\frac{2 s + 1}{s ^{2}}

What is the derivative of 6/((6-x^6)^{3/2)} ?
The derivative of 6/((6-x^6)^{3/2)} is (54x^5)/((6-x^6)^{5/2)}
What is the first derivative of 6/((6-x^6)^{3/2)} ?
The first derivative of 6/((6-x^6)^{3/2)} is (54x^5)/((6-x^6)^{5/2)}