What is the derivative of 1/(sqrt(10x+11)) ?

The derivative of 1/(sqrt(10x+11)) is -5/((10x+11)^{3/2)}

What is the first derivative of 1/(sqrt(10x+11)) ?

The first derivative of 1/(sqrt(10x+11)) is -5/((10x+11)^{3/2)}

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\frac{d}{d x} (\frac{1}{10 x + 11})

- \frac{5}{( 10 x + 11 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{10 x + 11})

Apply exponent rule:

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

= \frac{d}{d x} ((10 x + 11)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \frac{d}{d x} (10 x + 11)

= - \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \frac{d}{d x} (10 x + 11)

\frac{d}{d x} (10 x + 11) = 10

= - \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \cdot 10

Simplify

- \frac{1}{2 ( 10 x + 11 ) ^{\frac{3}{2}}} \cdot 10 : - \frac{5}{( 10 x + 11 ) ^{\frac{3}{2}}}

= - \frac{5}{( 10 x + 11 ) ^{\frac{3}{2}}}

What is the derivative of 1/(sqrt(10x+11)) ?
The derivative of 1/(sqrt(10x+11)) is -5/((10x+11)^{3/2)}
What is the first derivative of 1/(sqrt(10x+11)) ?
The first derivative of 1/(sqrt(10x+11)) is -5/((10x+11)^{3/2)}