What is the derivative of 1/(sqrt(16-x^2-5x)) ?

The derivative of 1/(sqrt(16-x^2-5x)) is -(-2x-5)/(2(16-x^2-5x)^{3/2)}

What is the first derivative of 1/(sqrt(16-x^2-5x)) ?

The first derivative of 1/(sqrt(16-x^2-5x)) is -(-2x-5)/(2(16-x^2-5x)^{3/2)}

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\frac{d}{d x} (\frac{1}{16 - x ^{2} - 5 x})

- \frac{- 2 x - 5}{2 ( 16 - x ^{2} - 5 x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{16 - x ^{2} - 5 x})

Apply exponent rule:

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

= \frac{d}{d x} ((16 - x^{2} - 5 x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 16 - x ^{2} - 5 x ) ^{\frac{3}{2}}} \frac{d}{d x} (16 - x^{2} - 5 x)

= - \frac{1}{2 ( 16 - x ^{2} - 5 x ) ^{\frac{3}{2}}} \frac{d}{d x} (16 - x^{2} - 5 x)

\frac{d}{d x} (16 - x^{2} - 5 x) = - 2 x - 5

= - \frac{1}{2 ( 16 - x ^{2} - 5 x ) ^{\frac{3}{2}}} (- 2 x - 5)

Simplify

- \frac{1}{2 ( 16 - x ^{2} - 5 x ) ^{\frac{3}{2}}} (- 2 x - 5) : - \frac{- 2 x - 5}{2 ( 16 - x ^{2} - 5 x ) ^{\frac{3}{2}}}

= - \frac{- 2 x - 5}{2 ( 16 - x ^{2} - 5 x ) ^{\frac{3}{2}}}

\int_{2}^{5} (\frac{3 x + 3}{x ^{2}}) d x

\int sin (5 x) cos (8 x) d x

\int x (x - 1) d x

\int_{1}^{\infty} \frac{n}{n ^{2} + 1}

x^{\frac{1}{2}}

What is the derivative of 1/(sqrt(16-x^2-5x)) ?
The derivative of 1/(sqrt(16-x^2-5x)) is -(-2x-5)/(2(16-x^2-5x)^{3/2)}
What is the first derivative of 1/(sqrt(16-x^2-5x)) ?
The first derivative of 1/(sqrt(16-x^2-5x)) is -(-2x-5)/(2(16-x^2-5x)^{3/2)}