What is (\partial)/(\partial x)(1/(x^2)+y) ?

The answer to (\partial)/(\partial x)(1/(x^2)+y) is -2/(x^3)

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(\partial)/(\partial x)(1/(x^2)+y)

\frac{\partial}{\partial x} (\frac{1}{x ^{2}} + y)

- \frac{2}{x ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x ^{2}} + y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

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

= - \frac{2}{x ^{3}} + 0

Simplify

= - \frac{2}{x ^{3}}

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

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0, y^{^{'}} (0) = 4

\frac{\partial}{\partial x} (sin (x) cosh (y))

\frac{d y}{d x} = 1 + x + y + x \cdot y

x \to \infty lim ((1 + \frac{5}{x})^{\frac{x}{7}})

What is (\partial)/(\partial x)(1/(x^2)+y) ?
The answer to (\partial)/(\partial x)(1/(x^2)+y) is -2/(x^3)