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Popular >

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

Solution

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

Solution

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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(dy)/(dx)+y=sin(x)

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Frequently Asked Questions (FAQ)

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