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)}

derivative of

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

- \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}}}

\int \frac{2 x ^{2}}{1 - 6 x ^{3}} d x

\frac{\partial}{\partial y} (x y^{3} - x^{2})

\int \frac{5 x ^{4}}{x ^{5} - 3} d x

a re a y = x^{2} - 4, y = - 2 x

\frac{d}{d x} (e^{\frac{x ^{3}}{3}})

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)}