What is the derivative of ((x^8))/(8(1-x^2)^4) ?

The derivative of ((x^8))/(8(1-x^2)^4) is (x^7)/((1-x^2)^5)

What is the first derivative of ((x^8))/(8(1-x^2)^4) ?

The first derivative of ((x^8))/(8(1-x^2)^4) is (x^7)/((1-x^2)^5)

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derivative of

\frac{( x ^{8} )}{8 ( 1 - x ^{2} ) ^{4}}

\frac{x ^{7}}{( 1 - x ^{2} ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{x ^{8}}{8 ( 1 - x ^{2} ) ^{4}})

Take the constant out:

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

= \frac{1}{8} \frac{d}{d x} (\frac{x ^{8}}{( 1 - x ^{2} ) ^{4}})

Apply the Quotient Rule:

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

= \frac{1}{8} \cdot \frac{\frac{d}{d x} ( x ^{8} ) ( 1 - x ^{2} ) ^{4} - \frac{d}{d x} ( ( 1 - x ^{2} ) ^{4} ) x ^{8}}{( ( 1 - x ^{2} ) ^{4} ) ^{2}}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} ((1 - x^{2})^{4}) = - 8 x (1 - x^{2})^{3}

= \frac{1}{8} \cdot \frac{8 x ^{7} ( 1 - x ^{2} ) ^{4} - ( - 8 x ( 1 - x ^{2} ) ^{3} ) x ^{8}}{( ( 1 - x ^{2} ) ^{4} ) ^{2}}

Simplify

\frac{1}{8} \cdot \frac{8 x ^{7} ( 1 - x ^{2} ) ^{4} - ( - 8 x ( 1 - x ^{2} ) ^{3} ) x ^{8}}{( ( 1 - x ^{2} ) ^{4} ) ^{2}} : \frac{x ^{7}}{( 1 - x ^{2} ) ^{5}}

= \frac{x ^{7}}{( 1 - x ^{2} ) ^{5}}

What is the derivative of ((x^8))/(8(1-x^2)^4) ?
The derivative of ((x^8))/(8(1-x^2)^4) is (x^7)/((1-x^2)^5)
What is the first derivative of ((x^8))/(8(1-x^2)^4) ?
The first derivative of ((x^8))/(8(1-x^2)^4) is (x^7)/((1-x^2)^5)