What is (\partial)/(\partial x)(x^4+xy^3) ?

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

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(\partial)/(\partial x)(x^4+xy^3)

\frac{\partial}{\partial x} (x^{4} + x y^{3})

4 x^{3} + y^{3}

Solution steps

\frac{\partial}{\partial x} (x^{4} + x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

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

x \to 0 + lim (\frac{e ^{x}}{x})

x \to 5 lim (8 x + 9)

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\int \frac{1}{x ( ln ( x ) ) ^{9}} d x

\frac{\partial}{\partial x} (x^{2} - 2 x y + 3 y^{2} - 8 y)

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