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

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

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

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

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

Solution steps

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

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

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

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

\frac{d}{d x} (3 x^{2} - 4 x - 5)

\frac{( - s - 1 )}{s ^{2} + s + 1}

\frac{d}{d x} (\frac{10}{x})

y^{^{'}} - \frac{3}{2} y = - \frac{3}{2} t

\frac{d}{d x} (x e^{- 10 x})

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