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Popular >

derivative of (1+4x)^{1/2}

Solution

derivative of

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

Solution

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

Solution steps

\frac{d}{d x} ((1 + 4 x)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 1 + 4 x ) ^{\frac{1}{2}}} \frac{d}{d x} (1 + 4 x)

= \frac{1}{2 ( 1 + 4 x ) ^{\frac{1}{2}}} \frac{d}{d x} (1 + 4 x)

\frac{d}{d x} (1 + 4 x) = 4

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

Simplify

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

= \frac{2}{( 1 + 4 x ) ^{\frac{1}{2}}}

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\frac{4 s}{( s + 1 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (1+4x)^{1/2} ?
The derivative of (1+4x)^{1/2} is 2/((1+4x)^{1/2)}
What is the first derivative of (1+4x)^{1/2} ?
The first derivative of (1+4x)^{1/2} is 2/((1+4x)^{1/2)}