What is the derivative of y= 4/((4-x^4)^{3/2)} ?

The derivative of y= 4/((4-x^4)^{3/2)} is (24x^3)/((4-x^4)^{5/2)}

What is the first derivative of y= 4/((4-x^4)^{3/2)} ?

The first derivative of y= 4/((4-x^4)^{3/2)} is (24x^3)/((4-x^4)^{5/2)}

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derivative of

y = \frac{4}{( 4 - x ^{4} ) ^{\frac{3}{2}}}

\frac{24 x ^{3}}{( 4 - x ^{4} ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{( 4 - x ^{4} ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((4 - x^{4})^{- \frac{3}{2}})

Apply the chain rule:

- \frac{3}{2 ( 4 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (4 - x^{4})

= - \frac{3}{2 ( 4 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (4 - x^{4})

\frac{d}{d x} (4 - x^{4}) = - 4 x^{3}

= 4 (- \frac{3}{2 ( 4 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3}))

Simplify

4 (- \frac{3}{2 ( 4 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3})) : \frac{24 x ^{3}}{( 4 - x ^{4} ) ^{\frac{5}{2}}}

= \frac{24 x ^{3}}{( 4 - x ^{4} ) ^{\frac{5}{2}}}

What is the derivative of y= 4/((4-x^4)^{3/2)} ?
The derivative of y= 4/((4-x^4)^{3/2)} is (24x^3)/((4-x^4)^{5/2)}
What is the first derivative of y= 4/((4-x^4)^{3/2)} ?
The first derivative of y= 4/((4-x^4)^{3/2)} is (24x^3)/((4-x^4)^{5/2)}