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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 4 x + 3

x - \frac{π}{2}, 1

t \to 0 lim (tan (5 t))

\frac{d}{d x} (\frac{2 x - 3}{3 x + 4})

\int \frac{2}{x ^{6}} d x

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