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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y = (x + 2)^{2}

\frac{d}{d x} (\frac{1}{( a \cdot cos ( x ) + b \cdot sin ( x ) )})

y = 5 e^{3 x}

((3 x - 2)^{4})^{^{'}}

(1 + x)^{5}

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