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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x ^{2} + 2 x + 1}{x ^{2}} d x

sin (x), 3

x \to 2 lim (4 x + 1)

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

\int e^{x^{3}} d x

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