What is (\partial)/(\partial x)(4x^3y-ysin(x)) ?

The answer to (\partial)/(\partial x)(4x^3y-ysin(x)) is 12yx^2-ycos(x)

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(\partial)/(\partial x)(4x^3y-ysin(x))

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

12 y x^{2} - y cos (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{3} y) = 12 y x^{2}

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

= 12 y x^{2} - y cos (x)

\int \frac{1}{25 x ^{2} - 16} d x

x \to 0 + lim (x ln (3 x))

\frac{\partial}{\partial z} (- 2 x y)

\int 3 x^{2} cos (6 x) d x

\frac{d}{d x} (ln (x^{2}) - \frac{1}{x ^{2}} - 5)

What is (\partial)/(\partial x)(4x^3y-ysin(x)) ?
The answer to (\partial)/(\partial x)(4x^3y-ysin(x)) is 12yx^2-ycos(x)