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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int_{0}^{2} x \cdot 3^{x} d x

\int cot^{3} (x) \cdot csc^{2} (x) d x

\int 4 x^{3} + x^{2} d x

\int x^{3} 2 x + 1 d x

\frac{d}{d x} (sin (x) + cos (x) + tan (x))

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