What is (\partial)/(\partial x)(tan(x/y)) ?

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} + 9 y = sec^{2} (3 t)

x \to - 19 + lim (8 x + 154)

\int_{0}^{π} x sin (x) cos (x) d x

(3 x y + y^{2}) + (x^{2} + x y) \frac{d y}{d x} = 0

\int (tan^{2} (x)) d x

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