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

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

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

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

5 x^{4} y^{3}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 5 x^{4} y^{3}

f (x) = 3 e^{x} + 2 x, (0, 3)

y^{^{'}} = \frac{( 2 x ^{4} + y ^{4} )}{x y ^{3}}

\int_{1}^{2} \frac{5 ln ( x )}{x ^{2}} d x

\frac{\partial}{\partial x} (t)

\frac{d}{d x} (\frac{( 3 x + 1 )}{tan ( x )})

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