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Popular >

derivative of f(x)=sin(1/(x^2))

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (cos^6(x))/(sin^{10)(x)}

\int \frac{cos ^{6} ( x )}{sin ^{10} ( x )} d x

y^{''}+(a_{1^2}pi^2)/(a_{2)^2}a_{3}^2y=0

y^{^{''}} + \frac{a _{1^{2}} π ^{2}}{a _{2}^{2}} a_{3}^{2} y = 0

inverse oflaplace sin(s)inverse laplace

sin (s)

integral of-e^x+sin(2x)

\int - e^{x} + sin (2 x) d x

integral from 0 to 3 of cos((nxpi)/3)

\int_{0}^{3} cos (\frac{n x π}{3}) d x

Frequently Asked Questions (FAQ)

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