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

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

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

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

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derivative of

\frac{5}{x + 5}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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