What is (\partial)/(\partial x)(4(xy)^2) ?

The answer to (\partial)/(\partial x)(4(xy)^2) is 8xy^2

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(\partial)/(\partial x)(4(xy)^2)

\frac{\partial}{\partial x} (4 (x y)^{2})

8 x y^{2}

Solution steps

\frac{\partial}{\partial x} (4 (x y)^{2})

Simplify

4 (x y)^{2} : 4 x^{2} y^{2}

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 4 y^{2} \cdot 2 x^{2 - 1}

Simplify

= 8 x y^{2}

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) (x + 7 x^{3}))

\int_{- 1}^{1} x^{2} - 2 x + 3 d x

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

\int_{0}^{\frac{π}{4}} \frac{1}{cos ( x )} d x

\frac{\partial}{\partial x} (cos (x^{3}))

What is (\partial)/(\partial x)(4(xy)^2) ?
The answer to (\partial)/(\partial x)(4(xy)^2) is 8xy^2