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

The derivative of sin(1/(x^2+1)) is -(2xcos(1/(x^2+1)))/((x^2+1)^2)

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

The first derivative of sin(1/(x^2+1)) is -(2xcos(1/(x^2+1)))/((x^2+1)^2)

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derivative of

sin (\frac{1}{x ^{2} + 1})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{sin ( x ) - x}{x ^{2}}

(- 2 x y 2 - 1 y) d x + (- 2 x 2 y + 1 x) d y = 0

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

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

f (x) = 9 ln (9 + 2 x^{2})

What is the derivative of sin(1/(x^2+1)) ?
The derivative of sin(1/(x^2+1)) is -(2xcos(1/(x^2+1)))/((x^2+1)^2)
What is the first derivative of sin(1/(x^2+1)) ?
The first derivative of sin(1/(x^2+1)) is -(2xcos(1/(x^2+1)))/((x^2+1)^2)