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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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