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Popular >

derivative of sin(1/(sqrt(x)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (xe^x)/2

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

(\partial)/(\partial x)(ln(x+3y+7z))

\frac{\partial}{\partial x} (ln (x + 3 y + 7 z))

integral of tan^3(x)(sec(x))^{3/2}

\int tan^{3} (x) (sec (x))^{\frac{3}{2}} d x

(\partial)/(\partial y)(2y^2+3x)

\frac{\partial}{\partial y} (2 y^{2} + 3 x)

limit as x approaches 0 of 3/0

x \to 0 lim (\frac{3}{0})

Frequently Asked Questions (FAQ)

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