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Popular >

derivative of sin(5/x)

Solution

\frac{d}{d x} (sin (\frac{5}{x}))

Solution

- \frac{5 cos ( \frac{5}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (sin (\frac{5}{x}))

Apply the chain rule:

cos (\frac{5}{x}) \frac{d}{d x} (\frac{5}{x})

= cos (\frac{5}{x}) \frac{d}{d x} (\frac{5}{x})

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

= cos (\frac{5}{x}) (- \frac{5}{x ^{2}})

Simplify

cos (\frac{5}{x}) (- \frac{5}{x ^{2}}) : - \frac{5 cos ( \frac{5}{x} )}{x ^{2}}

= - \frac{5 cos ( \frac{5}{x} )}{x ^{2}}

Popular Examples

(\partial)/(\partial x)(xcos(z))

\frac{\partial}{\partial x} (x cos (z))

derivative of 4x-5x^{9/10}

\frac{d}{d x} (4 x - 5 x^{\frac{9}{10}})

(3 t)^{^{'}}

area 2x^2,8x^2,5-3x,0 area

2 x^{2}, 8 x^{2}, 5 - 3 x, 0

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

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

Frequently Asked Questions (FAQ)

What is the derivative of sin(5/x) ?
The derivative of sin(5/x) is -(5cos(5/x))/(x^2)
What is the first derivative of sin(5/x) ?
The first derivative of sin(5/x) is -(5cos(5/x))/(x^2)