What is (\partial)/(\partial x)(x+1/y) ?

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

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(\partial)/(\partial x)(x+1/y)

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

1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

= 1 + 0

Simplify

= 1

\frac{( y ^{4} - x ^{2} ) d y}{d x} = - x y

\int \frac{9 + t + t ^{2}}{t} d t

\int sin (x) \cdot e^{c o s (x)} d x

\frac{d}{d x} (\frac{30}{x ^{4}})

y = x^{2} (4 x^{4} + 5 x^{3} - 16)

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