What is (\partial)/(\partial x)(x^3-xsin(y)) ?

The answer to (\partial)/(\partial x)(x^3-xsin(y)) is 3x^2-sin(y)

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(\partial)/(\partial x)(x^3-xsin(y))

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

3 x^{2} - sin (y)

Solution steps

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

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

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

= 3 x^{2} - sin (y)

\int_{- 1}^{0} x^{3} - x d x

\int x (16 - x^{2}) d x

x \to 2 lim (\frac{5 x}{x - 2})

\int e^{2 θ} sin (3 θ) d θ

(ln (f (x)))^{'}

What is (\partial)/(\partial x)(x^3-xsin(y)) ?
The answer to (\partial)/(\partial x)(x^3-xsin(y)) is 3x^2-sin(y)