What is the derivative of 9/((9-x^8)^{3/2)} ?

The derivative of 9/((9-x^8)^{3/2)} is (108x^7)/((9-x^8)^{5/2)}

What is the first derivative of 9/((9-x^8)^{3/2)} ?

The first derivative of 9/((9-x^8)^{3/2)} is (108x^7)/((9-x^8)^{5/2)}

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derivative of

\frac{9}{( 9 - x ^{8} ) ^{\frac{3}{2}}}

\frac{108 x ^{7}}{( 9 - x ^{8} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{9}{( 9 - x ^{8} ) ^{\frac{3}{2}}})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{( 9 - x ^{8} ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= 9 \frac{d}{d x} ((9 - x^{8})^{- \frac{3}{2}})

Apply the chain rule:

- \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} \frac{d}{d x} (9 - x^{8})

= - \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} \frac{d}{d x} (9 - x^{8})

\frac{d}{d x} (9 - x^{8}) = - 8 x^{7}

= 9 (- \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} (- 8 x^{7}))

Simplify

9 (- \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} (- 8 x^{7})) : \frac{108 x ^{7}}{( 9 - x ^{8} ) ^{\frac{5}{2}}}

= \frac{108 x ^{7}}{( 9 - x ^{8} ) ^{\frac{5}{2}}}

\int_{3}^{5} \frac{x ^{2}}{8} d x

n = 1 \sum \infty \frac{n}{1000 n + 1}

\frac{d}{d x} (3^{x} x^{3})

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

\frac{d ^{4}}{d x ^{4}} (13 e^{x^{2}})

What is the derivative of 9/((9-x^8)^{3/2)} ?
The derivative of 9/((9-x^8)^{3/2)} is (108x^7)/((9-x^8)^{5/2)}
What is the first derivative of 9/((9-x^8)^{3/2)} ?
The first derivative of 9/((9-x^8)^{3/2)} is (108x^7)/((9-x^8)^{5/2)}