What is the derivative of (4+x^2^{-1}) ?

The derivative of (4+x^2^{-1}) is -(2x)/((4+x^2)^2)

What is the first derivative of (4+x^2^{-1}) ?

The first derivative of (4+x^2^{-1}) is -(2x)/((4+x^2)^2)

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\frac{d}{d x} ((4 + x^{2})^{- 1})

- \frac{2 x}{( 4 + x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} ((4 + x^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 4 + x ^{2} ) ^{2}} \frac{d}{d x} (4 + x^{2})

= - \frac{1}{( 4 + x ^{2} ) ^{2}} \frac{d}{d x} (4 + x^{2})

\frac{d}{d x} (4 + x^{2}) = 2 x

= - \frac{1}{( 4 + x ^{2} ) ^{2}} \cdot 2 x

Simplify

- \frac{1}{( 4 + x ^{2} ) ^{2}} \cdot 2 x : - \frac{2 x}{( 4 + x ^{2} ) ^{2}}

= - \frac{2 x}{( 4 + x ^{2} ) ^{2}}

\int (x^{8} - \frac{2 x ^{5}}{7} - 5) d x

y^{^{'}} = \frac{x ^{2} + x y + y ^{2}}{x ^{2}}

d y = (x - 2 x y) d x

x^{2} + 4 x - 8

x \to 0 + lim (x^{5} ln (x))

What is the derivative of (4+x^2^{-1}) ?
The derivative of (4+x^2^{-1}) is -(2x)/((4+x^2)^2)
What is the first derivative of (4+x^2^{-1}) ?
The first derivative of (4+x^2^{-1}) is -(2x)/((4+x^2)^2)