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

The answer to (\partial)/(\partial x)(4x^4y) is 16x^3y

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

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

16 x^{3} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 16 x^{3} y

\int 2 x \cdot cos (x) d x

(3, 6), (5, 5)

\frac{d ^{2}}{d x ^{2}} (\frac{6 x ^{5}}{5} - 3 x)

y^{^{''}} - 6 y^{^{'}} + 10 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

7 x^{2} + 4 x - 5

What is (\partial)/(\partial x)(4x^4y) ?
The answer to (\partial)/(\partial x)(4x^4y) is 16x^3y