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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\int_{10}^{13} 2 x d x

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(dy)/(dx)+y/(x+2)=5(x-2)y^{1/2}

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Frequently Asked Questions (FAQ)

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