What is the derivative of 5/(x+10) ?

The derivative of 5/(x+10) is -5/((x+10)^2)

What is the first derivative of 5/(x+10) ?

The first derivative of 5/(x+10) is -5/((x+10)^2)

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\frac{d}{d x} (\frac{5}{x + 10})

- \frac{5}{( x + 10 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5}{x + 10})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{x + 10})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((x + 10)^{- 1})

Apply the chain rule:

- \frac{1}{( x + 10 ) ^{2}} \frac{d}{d x} (x + 10)

= - \frac{1}{( x + 10 ) ^{2}} \frac{d}{d x} (x + 10)

\frac{d}{d x} (x + 10) = 1

= 5 (- \frac{1}{( x + 10 ) ^{2}} \cdot 1)

Simplify

5 (- \frac{1}{( x + 10 ) ^{2}} \cdot 1) : - \frac{5}{( x + 10 ) ^{2}}

= - \frac{5}{( x + 10 ) ^{2}}

f (x) = e^{9 x}

\frac{d}{d x} (e^{- x} \cdot cos (x))

\frac{1}{s ^{2} + s + 2}

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

What is the derivative of 5/(x+10) ?
The derivative of 5/(x+10) is -5/((x+10)^2)
What is the first derivative of 5/(x+10) ?
The first derivative of 5/(x+10) is -5/((x+10)^2)