What is the derivative of 7/((7-x^8)^{3/2)} ?

The derivative of 7/((7-x^8)^{3/2)} is (84x^7)/((7-x^8)^{5/2)}

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

The first derivative of 7/((7-x^8)^{3/2)} is (84x^7)/((7-x^8)^{5/2)}

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derivative of

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

\frac{84 x ^{7}}{( 7 - x ^{8} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{7}{( 7 - x ^{8} ) ^{\frac{3}{2}}})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{1}{( 7 - x ^{8} ) ^{\frac{3}{2}}})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

7 (- \frac{3}{2 ( 7 - x ^{8} ) ^{\frac{5}{2}}} (- 8 x^{7})) : \frac{84 x ^{7}}{( 7 - x ^{8} ) ^{\frac{5}{2}}}

= \frac{84 x ^{7}}{( 7 - x ^{8} ) ^{\frac{5}{2}}}

(sin^{2} (x) + 1)^{5}

2 t - sin (2 t)

\int cos^{3} (x) d x

\int (x^{3} + 3 x) e^{- 6 x} d x

\frac{\partial}{\partial y} (x e^{x^{2} - y^{2}})

What is the derivative of 7/((7-x^8)^{3/2)} ?
The derivative of 7/((7-x^8)^{3/2)} is (84x^7)/((7-x^8)^{5/2)}
What is the first derivative of 7/((7-x^8)^{3/2)} ?
The first derivative of 7/((7-x^8)^{3/2)} is (84x^7)/((7-x^8)^{5/2)}