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

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

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

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

3 x^{3} cos (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 3 x^{3} cos (y)

Simplify

= 3 x^{3} cos (y)

\frac{d y}{d x} = \frac{y ^{3}}{x}

\int 8 + tan^{2} (x) d x

x \to 6 lim (4 x + ∣ x - 6 ∣)

d er i v a t i v e f (x) = x^{3} + x^{2} - 2 x

x \to 2 lim (\frac{2 x + 1}{x + 2})

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