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Popular >

(\partial)/(\partial y)(tan(y/x))

Solution

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

Solution

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (\frac{y}{x}) = \frac{1}{x}

= sec^{2} (\frac{y}{x}) \frac{1}{x}

Simplify

sec^{2} (\frac{y}{x}) \frac{1}{x} : \frac{sec ^{2} ( \frac{y}{x} )}{x}

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

Popular Examples

f (x) = sin (7 x)

slope of 1/3*t^3-9*t+2 slope

\frac{1}{3} \cdot t^{3} - 9 \cdot t + 2

integral of xsqrt(1+1/(4x))

\int x 1 + \frac{1}{4 x} d x

tangent of sqrt(3x+25),\at x=-3 tangent of

3 x + 25, at x = - 3

integral of (2x-1)ln(5x)

\int (2 x - 1) ln (5 x) d x

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial y)(tan(y/x)) ?
The answer to (\partial)/(\partial y)(tan(y/x)) is (sec^2(y/x))/x