What is (\partial)/(\partial x)(3x^4y^2) ?

The answer to (\partial)/(\partial x)(3x^4y^2) is 12x^3y^2

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(\partial)/(\partial x)(3x^4y^2)

\frac{\partial}{\partial x} (3 x^{4} y^{2})

12 x^{3} y^{2}

Solution steps

\frac{\partial}{\partial x} (3 x^{4} y^{2})

Treat

y

as a constant

Take the constant out:

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

= 3 y^{2} \frac{\partial}{\partial x} (x^{4})

Apply the Power Rule:

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

= 3 y^{2} \cdot 4 x^{4 - 1}

Simplify

= 12 x^{3} y^{2}

\int \frac{3 x}{4 - x} d x

\int x^{9} cos (x^{5}) d x

\int (4 csc (x) cot (x) + 2 sec^{2} (x)) d x

f (x) = \frac{1}{x ^{3}}

f (x) = 20 x^{2} + 14 x - 2 x^{2}

What is (\partial)/(\partial x)(3x^4y^2) ?
The answer to (\partial)/(\partial x)(3x^4y^2) is 12x^3y^2