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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{1 - 5 x}{x + 3}

\frac{d}{d x} (x^{\frac{8}{x}})

x \to π lim (ln (cos (x) - 8))

cos (5 t)

x \to 2 lim (\frac{x}{( - x + 2 ) ^{2}})

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