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Popular >

derivative of (3x+1^{1/2})

Solution

\frac{d}{d x} ((3 x + 1)^{\frac{1}{2}})

Solution

\frac{3}{2 ( 3 x + 1 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((3 x + 1)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 3 x + 1 ) ^{\frac{1}{2}}} \frac{d}{d x} (3 x + 1)

= \frac{1}{2 ( 3 x + 1 ) ^{\frac{1}{2}}} \frac{d}{d x} (3 x + 1)

\frac{d}{d x} (3 x + 1) = 3

= \frac{1}{2 ( 3 x + 1 ) ^{\frac{1}{2}}} \cdot 3

Simplify

\frac{1}{2 ( 3 x + 1 ) ^{\frac{1}{2}}} \cdot 3 : \frac{3}{2 ( 3 x + 1 ) ^{\frac{1}{2}}}

= \frac{3}{2 ( 3 x + 1 ) ^{\frac{1}{2}}}

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Frequently Asked Questions (FAQ)

What is the derivative of (3x+1^{1/2}) ?
The derivative of (3x+1^{1/2}) is 3/(2(3x+1)^{1/2)}
What is the first derivative of (3x+1^{1/2}) ?
The first derivative of (3x+1^{1/2}) is 3/(2(3x+1)^{1/2)}