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}

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\frac{d}{d x} (sin^{2} (3 + x))

\frac{d y}{d x} = (\frac{( 4 y + 3 )}{8 x + 5})^{2}

x \to 6 lim (4 x + ∣ x - 6 ∣)

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