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

The derivative of f(x)=(3x+1)^{1/2} is 3/(2(3x+1)^{1/2)}

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

The first derivative of f(x)=(3x+1)^{1/2} is 3/(2(3x+1)^{1/2)}

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derivative of

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

\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}}}

\int x + 5 d x

sec^{2} (π t)

(1, - 6), (4, - 6)

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