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

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

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

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

12 x^{2} y^{2}

Solution steps

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

Apply the Power Rule:

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

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

Simplify

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

\int (1 - 2 x^{2}) d x

\int (6 x^{2} - 7 x + 3) d x

\int (tan (\frac{x}{6}))^{5} d x

\int \frac{ln ( x )}{( 1 - ln ^{2} ( x ) ) x} d x

y = 6 x, y = x^{2} - 7

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