What is the derivative of 1/(sqrt(x^2+3)) ?

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

What is the first derivative of 1/(sqrt(x^2+3)) ?

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{cos ( x )}{8 - sin ( x )} d x

\int \frac{7}{9 + 16 r ^{2}} d r

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1), y (0) = 0

x \to 3 - lim (\frac{x + 5}{x - 3})

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