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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

taylor x^{11/2},x=1 taylor

x^{\frac{11}{2}}, x = 1

tangent of f(x)=-3x^{3/2}-1,\at x=4 tangent of

f (x) = - 3 x^{\frac{3}{2}} - 1, at x = 4

derivative of f(x)=e^{1-2x}(x+cos(2x))derivative of

f (x) = e^{1 - 2 x} (x + cos (2 x))

area f(x)=x^3+x^2+1,g(x)=2x+1 area

f (x) = x^{3} + x^{2} + 1, g (x) = 2 x + 1

integral of 1/(25-36x^2)

\int \frac{1}{25 - 36 x ^{2}} d x

Frequently Asked Questions (FAQ)

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