What is (\partial)/(\partial x)(x^5y) ?

The answer to (\partial)/(\partial x)(x^5y) is 5x^4y

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(\partial)/(\partial x)(x^5y)

\frac{\partial}{\partial x} (x^{5} y)

5 x^{4} y

Solution steps

\frac{\partial}{\partial x} (x^{5} y)

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (x^{5})

Apply the Power Rule:

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

= y \cdot 5 x^{5 - 1}

Simplify

= 5 x^{4} y

\int \frac{4 x ^{2} + 2 x + 8}{x ( x ^{2} + 2 ) ^{2}} d x

x \to + 1 lim (- \frac{3}{x - 1})

x, at x = 25

\frac{\partial}{\partial x} (sin (- x) cos (4 y))

y^{^{'}} = 2 y + x e^{x}, y (0) = - 1

What is (\partial)/(\partial x)(x^5y) ?
The answer to (\partial)/(\partial x)(x^5y) is 5x^4y