What is the derivative of 4/((4-x^6)^{3/2)} ?

The derivative of 4/((4-x^6)^{3/2)} is (36x^5)/((4-x^6)^{5/2)}

What is the first derivative of 4/((4-x^6)^{3/2)} ?

The first derivative of 4/((4-x^6)^{3/2)} is (36x^5)/((4-x^6)^{5/2)}

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derivative of

\frac{4}{( 4 - x ^{6} ) ^{\frac{3}{2}}}

\frac{36 x ^{5}}{( 4 - x ^{6} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{4}{( 4 - x ^{6} ) ^{\frac{3}{2}}})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{( 4 - x ^{6} ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((4 - x^{6})^{- \frac{3}{2}})

Apply the chain rule:

- \frac{3}{2 ( 4 - x ^{6} ) ^{\frac{5}{2}}} \frac{d}{d x} (4 - x^{6})

= - \frac{3}{2 ( 4 - x ^{6} ) ^{\frac{5}{2}}} \frac{d}{d x} (4 - x^{6})

\frac{d}{d x} (4 - x^{6}) = - 6 x^{5}

= 4 (- \frac{3}{2 ( 4 - x ^{6} ) ^{\frac{5}{2}}} (- 6 x^{5}))

Simplify

4 (- \frac{3}{2 ( 4 - x ^{6} ) ^{\frac{5}{2}}} (- 6 x^{5})) : \frac{36 x ^{5}}{( 4 - x ^{6} ) ^{\frac{5}{2}}}

= \frac{36 x ^{5}}{( 4 - x ^{6} ) ^{\frac{5}{2}}}

x y^{^{'}} + y = - 2 x y^{2}

cos (e^{- 2 θ^{3}})

\frac{d}{d x} (4 x^{- \frac{3}{8}})

\int sin^{4} (2 x) cos^{4} (2 x) d x

f (x) = (4 x - 1) x^{\frac{9}{2}}

What is the derivative of 4/((4-x^6)^{3/2)} ?
The derivative of 4/((4-x^6)^{3/2)} is (36x^5)/((4-x^6)^{5/2)}
What is the first derivative of 4/((4-x^6)^{3/2)} ?
The first derivative of 4/((4-x^6)^{3/2)} is (36x^5)/((4-x^6)^{5/2)}