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

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

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

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

12 x^{3} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 12 x^{3} y

\frac{d}{d x} (\frac{4 x ^{4} - 7 x}{x ^{3} - 8})

f (x) = 2 x^{2} - 9 x + 10, at x = 3

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

\frac{d}{d x} (e^{(6 x - 7 x^{2})})

\int_{- 2}^{2} e^{- x^{2}} d x

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