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Popular >

derivative of tan(y/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

Popular Examples

limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42)

x \to 6 lim (\frac{x ^{2} + 11 x - 30}{x ^{2} - 13 x - 42})

derivative of csc^2(x)-1 derivative of

csc^{2} (x) - 1

area y=sqrt(x),y=2-x,y=0 area

y = x, y = 2 - x, y = 0

integral of tan(1)

\int tan (1) d x

derivative of (t+e^t)(2-sqrt(t))derivative of

(t + e^{t}) (2 - t)

Frequently Asked Questions (FAQ)

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