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)}

Popular >

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 sec (d) x d x

\int (\frac{2}{x} + \frac{x}{2}) d x

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

x \to 16 lim (x)

\frac{\partial}{\partial x} (sin (\frac{1}{1 + y}))

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)}