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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Expand

2 x (2 x + 1) - 2 x^{2} : 2 x^{2} + 2 x

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

Popular Examples

3y^{''}+13y^'+4y=0

3 y^{^{''}} + 13 y^{^{'}} + 4 y = 0

integral of (e^{2x})/(49+e^{4x)}

\int \frac{e ^{2 x}}{49 + e ^{4 x}} d x

(2 y - 9) d x + x d y = 0

integral of 1/(x^{1/3)+x^{1/4}}

\int \frac{1}{x ^{\frac{1}{3}} + x ^{\frac{1}{4}}} d x

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Frequently Asked Questions (FAQ)

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