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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

\frac{d}{d x} (1 + x) = 1

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

Simplify

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

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

\frac{s}{( s + 1 ) ^{2}}

\frac{d}{d z} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

\int \frac{sin ( \frac{1}{x} )}{x ^{2}} d x

\int x^{4} 4 + x^{5} d x

x \to 0 + lim (x^{2} + 3)

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