What is the derivative of ((x+1^5)/((1-x)^4)) ?

The derivative of ((x+1^5)/((1-x)^4)) is ((x+1)^4(-x+9))/((1-x)^5)

What is the first derivative of ((x+1^5)/((1-x)^4)) ?

The first derivative of ((x+1^5)/((1-x)^4)) is ((x+1)^4(-x+9))/((1-x)^5)

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\frac{d}{d x} (\frac{( x + 1 ) ^{5}}{( 1 - x ) ^{4}})

\frac{( x + 1 ) ^{4} ( - x + 9 )}{( 1 - x ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{( x + 1 ) ^{5}}{( 1 - x ) ^{4}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((x + 1)^{5}) = 5 (x + 1)^{4}

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

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

Simplify

\frac{5 ( x + 1 ) ^{4} ( 1 - x ) ^{4} - ( - 4 ( 1 - x ) ^{3} ) ( x + 1 ) ^{5}}{( ( 1 - x ) ^{4} ) ^{2}} : \frac{( x + 1 ) ^{4} ( - x + 9 )}{( 1 - x ) ^{5}}

= \frac{( x + 1 ) ^{4} ( - x + 9 )}{( 1 - x ) ^{5}}

What is the derivative of ((x+1^5)/((1-x)^4)) ?
The derivative of ((x+1^5)/((1-x)^4)) is ((x+1)^4(-x+9))/((1-x)^5)
What is the first derivative of ((x+1^5)/((1-x)^4)) ?
The first derivative of ((x+1^5)/((1-x)^4)) is ((x+1)^4(-x+9))/((1-x)^5)