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Popular >

derivative of cos(x/y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

- sin (\frac{x}{y}) \frac{d}{d x} (\frac{x}{y})

= - sin (\frac{x}{y}) \frac{d}{d x} (\frac{x}{y})

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Popular Examples

d/(da)(2sin(2a)+2cos^2(a))

\frac{d}{d a} (2 sin (2 a) + 2 cos^{2} (a))

inverse oflaplace 2/(s+1)+(16s)/(s^2+9)inverse laplace

\frac{2}{s + 1} + \frac{16 s}{s ^{2} + 9}

slope of (1.4)(3.5)slope

(1.4) (3.5)

inverse oflaplace 1/(s^2+3s)inverse laplace

\frac{1}{s ^{2} + 3 s}

derivative of (2x^8)

\frac{d}{d x} ((2 x)^{8})

Frequently Asked Questions (FAQ)

What is the derivative of cos(x/y) ?
The derivative of cos(x/y) is -(sin(x/y)(y-x\frac{dy)/(dx))}{y^2}
What is the first derivative of cos(x/y) ?
The first derivative of cos(x/y) is -(sin(x/y)(y-x\frac{dy)/(dx))}{y^2}