What is (\partial)/(\partial y)(x^2y^5) ?

The answer to (\partial)/(\partial y)(x^2y^5) is 5x^2y^4

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(\partial)/(\partial y)(x^2y^5)

\frac{\partial}{\partial y} (x^{2} y^{5})

5 x^{2} y^{4}

Solution steps

\frac{\partial}{\partial y} (x^{2} y^{5})

Treat

x

as a constant

Take the constant out:

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

= x^{2} \frac{\partial}{\partial y} (y^{5})

Apply the Power Rule:

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

= x^{2} \cdot 5 y^{5 - 1}

Simplify

= 5 x^{2} y^{4}

x \to 1 + lim (- 2)

y^{^{'}} + 2 y = x^{2} y^{3}

f (x) = x^{9} e^{x}

\frac{d}{d x} (in x^{2})

\int_{0}^{\frac{π}{4}} 49 sin^{2} (x) d x

What is (\partial)/(\partial y)(x^2y^5) ?
The answer to (\partial)/(\partial y)(x^2y^5) is 5x^2y^4