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

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

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(\partial)/(\partial x)(xe^y+x^4y+y^3)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (y^{3}) = 0

= e^{y} + 4 y x^{3} + 0

Simplify

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

\frac{d}{d x} (ln (x^{2} + y^{4}))

4 cos (5 t)

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

\frac{5 x}{x - 2}

y^{^{'}} = 6 x 9 - y^{2}

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