What is the derivative of 5/(sqrt(4+x)) ?

The derivative of 5/(sqrt(4+x)) is -5/(2(4+x)^{3/2)}

What is the first derivative of 5/(sqrt(4+x)) ?

The first derivative of 5/(sqrt(4+x)) is -5/(2(4+x)^{3/2)}

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\frac{d}{d x} (\frac{5}{4 + x})

- \frac{5}{2 ( 4 + x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{5}{4 + x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{1}{4 + x})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((4 + x)^{- \frac{1}{2}})

Apply the chain rule:

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

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

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

= 5 (- \frac{1}{2 ( 4 + x ) ^{\frac{3}{2}}} \cdot 1)

Simplify

5 (- \frac{1}{2 ( 4 + x ) ^{\frac{3}{2}}} \cdot 1) : - \frac{5}{2 ( 4 + x ) ^{\frac{3}{2}}}

= - \frac{5}{2 ( 4 + x ) ^{\frac{3}{2}}}

(4, 1), (7, 10)

\frac{d}{d x} (\frac{18}{x})

\frac{\partial}{\partial y} (2 cos (x) + cos (x + y))

\int 5 sin^{2} (r) cos (r) d r

x^{2 x + 1}

What is the derivative of 5/(sqrt(4+x)) ?
The derivative of 5/(sqrt(4+x)) is -5/(2(4+x)^{3/2)}
What is the first derivative of 5/(sqrt(4+x)) ?
The first derivative of 5/(sqrt(4+x)) is -5/(2(4+x)^{3/2)}