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Popular >

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

Solution

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

Solution

\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}}

Popular Examples

derivative of (6t)/(6+sqrt(t))derivative of

\frac{6 t}{6 + t}

(dy)/(dx)=xy+9x+2y+18

\frac{d y}{d x} = x y + 9 x + 2 y + 18

36y^{''}-60y^'+26y=0,y(4)=2,y^'(4)=5

36 y^{^{''}} - 60 y^{^{'}} + 26 y = 0, y (4) = 2, y^{^{'}} (4) = 5

derivative of ((x+2)(x^2-2x+4))/(x^3)derivative of

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

integral of 250(e^{-0.2x}-1)

\int 250 (e^{- 0.2 x} - 1) d x

Frequently Asked Questions (FAQ)

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