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

The derivative of-((2x^2+1)/((1-x^2)^{5/2)}) is -(3x(2x^2+3))/((1-x^2)^{7/2)}

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

The first derivative of-((2x^2+1)/((1-x^2)^{5/2)}) is -(3x(2x^2+3))/((1-x^2)^{7/2)}

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

- \frac{3 x ( 2 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

= - \frac{4 x ( 1 - x ^{2} ) ^{\frac{5}{2}} - ( - 5 x ( 1 - x ^{2} ) ^{\frac{3}{2}} ) ( 2 x ^{2} + 1 )}{( ( 1 - x ^{2} ) ^{\frac{5}{2}} ) ^{2}}

Simplify

- \frac{4 x ( 1 - x ^{2} ) ^{\frac{5}{2}} - ( - 5 x ( 1 - x ^{2} ) ^{\frac{3}{2}} ) ( 2 x ^{2} + 1 )}{( ( 1 - x ^{2} ) ^{\frac{5}{2}} ) ^{2}} : - \frac{3 x ( 2 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}

= - \frac{3 x ( 2 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}

x \frac{d y}{d x} = y^{2}

sin (4 x)

\int - \frac{e ^{4 x}}{4 x} d x

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

f (x) = x sin (2 x^{2})

What is the derivative of-((2x^2+1)/((1-x^2)^{5/2)}) ?
The derivative of-((2x^2+1)/((1-x^2)^{5/2)}) is -(3x(2x^2+3))/((1-x^2)^{7/2)}
What is the first derivative of-((2x^2+1)/((1-x^2)^{5/2)}) ?
The first derivative of-((2x^2+1)/((1-x^2)^{5/2)}) is -(3x(2x^2+3))/((1-x^2)^{7/2)}