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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 1 lim (\frac{x ^{5} - 1}{x - 1})

f (x) = x sin (2^{x})

\frac{1}{x} e^{y} tan (y) y^{^{'}} = e^{x + y}

\frac{\partial}{\partial y} (\frac{4 x}{x ^{2} + y ^{2}})

\int \frac{1}{2} (cos (x))^{2} d x

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