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

The answer to (\partial)/(\partial x)(1/2*x*y^2) is (y^2)/2

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(\partial)/(\partial x)(1/2xy^2)

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

\frac{y ^{2}}{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= \frac{1}{2} y^{2} \cdot 1

Simplify

\frac{1}{2} y^{2} \cdot 1 : \frac{y ^{2}}{2}

= \frac{y ^{2}}{2}

x \to \infty lim (\frac{4}{x} - 2)

100 x^{2} + 400 x + 5000

\int \frac{x}{x ^{4} + 6 x ^{2} + 10} d x

\int \frac{1}{4 - ( u + 3 )} d u

\frac{d}{d x} (2 sin^{2} (\frac{x}{2}))

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