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

The derivative of cos(1/(x^2)) is (2sin(1/(x^2)))/(x^3)

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

The first derivative of cos(1/(x^2)) is (2sin(1/(x^2)))/(x^3)

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

\frac{2 sin ( \frac{1}{x ^{2}} )}{x ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 sin ( \frac{1}{x ^{2}} )}{x ^{3}}

f (t) = \frac{t}{2}

\frac{d}{d x} (x^{0.25})

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

x \to + 1 lim (a r cos (x))

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

What is the derivative of cos(1/(x^2)) ?
The derivative of cos(1/(x^2)) is (2sin(1/(x^2)))/(x^3)
What is the first derivative of cos(1/(x^2)) ?
The first derivative of cos(1/(x^2)) is (2sin(1/(x^2)))/(x^3)