What is (\partial)/(\partial x)(x^3e^x+cos(y)) ?

The answer to (\partial)/(\partial x)(x^3e^x+cos(y)) is e^xx^3+3e^xx^2

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(\partial)/(\partial x)(x^3e^x+cos(y))

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

e^{x} x^{3} + 3 e^{x} x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{3} e^{x}) = 3 x^{2} e^{x} + e^{x} x^{3}

\frac{\partial}{\partial x} (cos (y)) = 0

= 3 x^{2} e^{x} + e^{x} x^{3} + 0

Simplify

= e^{x} x^{3} + 3 e^{x} x^{2}

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What is (\partial)/(\partial x)(x^3e^x+cos(y)) ?
The answer to (\partial)/(\partial x)(x^3e^x+cos(y)) is e^xx^3+3e^xx^2