Find dy/dx for the equation y sin 3x + y3 cos x + 5 = 0 using implicit differentiation.

Here are the solutions to the calculus problems:

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The equation is $y \sin 3x + y^3 \cos x + 5 = 0$. We need to find $\frac{dy}{dx}$ using implicit differentiation.

Step 1: Differentiate both sides of the equation with respect to $x$.

$$\frac{d}{dx}(y \sin 3x) + \frac{d}{dx}(y^3 \cos x) + \frac{d}{dx}(5) = \frac{d}{dx}(0)$$

Step 2: Apply the product rule and chain rule for differentiation.
For $\frac{d}{dx}(y \sin 3x)$:

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