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

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

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

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

3 x^{2} + cos (x y) y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 x^{2} + cos (x y) y

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