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

The answer to (\partial)/(\partial x)(5x^4y^2) is 20x^3y^2

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(\partial)/(\partial x)(5x^4y^2)

\frac{\partial}{\partial x} (5 x^{4} y^{2})

20 x^{3} y^{2}

Solution steps

\frac{\partial}{\partial x} (5 x^{4} y^{2})

Treat

y

as a constant

Take the constant out:

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

= 5 y^{2} \frac{\partial}{\partial x} (x^{4})

Apply the Power Rule:

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

= 5 y^{2} \cdot 4 x^{4 - 1}

Simplify

= 20 x^{3} y^{2}

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

x \to - 2 lim (\frac{sin ( x )}{2 x})

\int \frac{x + 1}{x ^{2} + 2 x + 3} d x

\int \frac{e ^{3 x}}{9 + 4 e ^{6 x}} d x

\frac{2}{s ^{5}}

What is (\partial)/(\partial x)(5x^4y^2) ?
The answer to (\partial)/(\partial x)(5x^4y^2) is 20x^3y^2