What is (\partial)/(\partial x)(x^3y^5) ?

The answer to (\partial)/(\partial x)(x^3y^5) is 3x^2y^5

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(\partial)/(\partial x)(x^3y^5)

\frac{\partial}{\partial x} (x^{3} y^{5})

3 x^{2} y^{5}

Solution steps

\frac{\partial}{\partial x} (x^{3} y^{5})

Treat

y

as a constant

Take the constant out:

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

= y^{5} \frac{\partial}{\partial x} (x^{3})

Apply the Power Rule:

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

= y^{5} \cdot 3 x^{3 - 1}

Simplify

= 3 x^{2} y^{5}

\frac{d}{d x} (3 x^{2} + 3 x - 4)

\int \frac{sin ( x )}{1 + x ^{2}} d x

(x^{12})^{5}

\frac{d}{d x} (\frac{1}{2} x - \frac{1}{4})

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

What is (\partial)/(\partial x)(x^3y^5) ?
The answer to (\partial)/(\partial x)(x^3y^5) is 3x^2y^5