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Popular >

derivative of f(x)= 1/(sqrt(x+4))

Solution

derivative of

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

Solution

- \frac{1}{2 ( x + 4 ) ^{\frac{3}{2}}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{2 ( x + 4 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 4)

= - \frac{1}{2 ( x + 4 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 4)

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

= - \frac{1}{2 ( x + 4 ) ^{\frac{3}{2}}} \cdot 1

Simplify

= - \frac{1}{2 ( x + 4 ) ^{\frac{3}{2}}}

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x \to 0 lim (\frac{cos ( x )}{x - \frac{π}{2}})

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)= 1/(sqrt(x+4)) ?
The derivative of f(x)= 1/(sqrt(x+4)) is -1/(2(x+4)^{3/2)}
What is the first derivative of f(x)= 1/(sqrt(x+4)) ?
The first derivative of f(x)= 1/(sqrt(x+4)) is -1/(2(x+4)^{3/2)}