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

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

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

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

y

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

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

= y \cdot 1

Simplify

= y

(f (x) (x)^{g (x)})^{'}

x \to 2 lim (\frac{4 x ^{2} - 2 x + 5}{x})

\int \frac{435}{3 x + 14} - 15 d x

f (x) = 3 x^{2} + 2 x, at x = 3

\int \frac{sin ( x )}{cos ^{3} ( x )} d x

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