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Popular >

derivative of tan(x/y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

sec^{2} (\frac{x}{y}) \frac{d}{d x} (\frac{x}{y})

= sec^{2} (\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}}

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

Popular Examples

sum from n=1 to infinity of 2/(4^{2n)}

n = 1 \sum \infty \frac{2}{4 ^{2 n}}

limit as h approaches 0 of ((7/(x+h)-7/x))/h

h \to 0 lim (\frac{( \frac{7}{x + h} - \frac{7}{x} )}{h})

limit as x approaches 1 of ln|x-1|

x \to 1 lim (ln ∣ x - 1 ∣)

(\partial ^2)/(\partial x^2)(2cos(xy^2))

\frac{\partial ^{2}}{\partial x ^{2}} (2 cos (x y^{2}))

((dy)/(dx))=(x+y+7)^2

(\frac{d y}{d x}) = (x + y + 7)^{2}

Frequently Asked Questions (FAQ)

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