What is (\partial)/(\partial y)(y/x+6x) ?

The answer to (\partial)/(\partial y)(y/x+6x) is 1/x

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(\partial)/(\partial y)(y/x+6x)

\frac{\partial}{\partial y} (\frac{y}{x} + 6 x)

\frac{1}{x}

Solution steps

\frac{\partial}{\partial y} (\frac{y}{x} + 6 x)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (\frac{y}{x}) + \frac{\partial}{\partial y} (6 x)

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

\frac{\partial}{\partial y} (6 x) = 0

= \frac{1}{x} + 0

Simplify

= \frac{1}{x}

\int \frac{1}{8 x ^{4}} d x

3^{x^{2} - 1}, at x = 2

\int \frac{1}{3} d x

\int 4 x^{- 2} + 3 x^{- 1} - 1 d x

x \to 2 π lim (sin (x))

What is (\partial)/(\partial y)(y/x+6x) ?
The answer to (\partial)/(\partial y)(y/x+6x) is 1/x