What is the derivative of y=(10)/((10-x^4)^{3/2)} ?

The derivative of y=(10)/((10-x^4)^{3/2)} is (60x^3)/((10-x^4)^{5/2)}

What is the first derivative of y=(10)/((10-x^4)^{3/2)} ?

The first derivative of y=(10)/((10-x^4)^{3/2)} is (60x^3)/((10-x^4)^{5/2)}

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derivative of

y = \frac{10}{( 10 - x ^{4} ) ^{\frac{3}{2}}}

\frac{60 x ^{3}}{( 10 - x ^{4} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{10}{( 10 - x ^{4} ) ^{\frac{3}{2}}})

Take the constant out:

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

= 10 \frac{d}{d x} (\frac{1}{( 10 - x ^{4} ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= 10 \frac{d}{d x} ((10 - x^{4})^{- \frac{3}{2}})

Apply the chain rule:

- \frac{3}{2 ( 10 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (10 - x^{4})

= - \frac{3}{2 ( 10 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (10 - x^{4})

\frac{d}{d x} (10 - x^{4}) = - 4 x^{3}

= 10 (- \frac{3}{2 ( 10 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3}))

Simplify

10 (- \frac{3}{2 ( 10 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3})) : \frac{60 x ^{3}}{( 10 - x ^{4} ) ^{\frac{5}{2}}}

= \frac{60 x ^{3}}{( 10 - x ^{4} ) ^{\frac{5}{2}}}

\int \frac{x ^{2} + x - 6}{x ^{2} - 9} d x

\int \frac{1}{( 95 - x ) ^{2}} d x

x \to - 2 lim (\frac{x}{x})

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

\int \frac{5 x}{2 x ^{3} + 6 x ^{2}} d x

What is the derivative of y=(10)/((10-x^4)^{3/2)} ?
The derivative of y=(10)/((10-x^4)^{3/2)} is (60x^3)/((10-x^4)^{5/2)}
What is the first derivative of y=(10)/((10-x^4)^{3/2)} ?
The first derivative of y=(10)/((10-x^4)^{3/2)} is (60x^3)/((10-x^4)^{5/2)}