What is the derivative of 1/((1-x^2^{3/2)}) ?

The derivative of 1/((1-x^2^{3/2)}) is (3x)/((1-x^2)^{5/2)}

What is the first derivative of 1/((1-x^2^{3/2)}) ?

The first derivative of 1/((1-x^2^{3/2)}) is (3x)/((1-x^2)^{5/2)}

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

\frac{3 x}{( 1 - x ^{2} ) ^{\frac{5}{2}}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{2 ( 1 - x ^{2} ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - x^{2})

= - \frac{3}{2 ( 1 - x ^{2} ) ^{\frac{5}{2}}} \frac{d}{d x} (1 - x^{2})

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

= - \frac{3}{2 ( 1 - x ^{2} ) ^{\frac{5}{2}}} (- 2 x)

Simplify

- \frac{3}{2 ( 1 - x ^{2} ) ^{\frac{5}{2}}} (- 2 x) : \frac{3 x}{( 1 - x ^{2} ) ^{\frac{5}{2}}}

= \frac{3 x}{( 1 - x ^{2} ) ^{\frac{5}{2}}}

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

\int_{0}^{\frac{3}{5}} 9 - 25 x^{2} d x

e^{- s} (\frac{1}{s ^{2}})

\int sin^{2} (3 x) d x

\int_{- 1}^{2} x d x

What is the derivative of 1/((1-x^2^{3/2)}) ?
The derivative of 1/((1-x^2^{3/2)}) is (3x)/((1-x^2)^{5/2)}
What is the first derivative of 1/((1-x^2^{3/2)}) ?
The first derivative of 1/((1-x^2^{3/2)}) is (3x)/((1-x^2)^{5/2)}