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

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

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

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

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derivative of

f (x) = \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}}

\int_{0}^{16} 0.8 (16 - x) d x

1 - 4 t^{2} d s + 2 1 - s^{2} d t = 0

\int (x^{2} - 5 x + 4) d x

\int cos (4 x) cos (2 x) d x

\frac{d}{d x} (a r (x) cos (x))

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