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

April 21, 2026Mathematics

ScanSolve AI Answer

April 21, 2026

Answer

\frac{d}{dx}(0) $$

Here are the solutions to the calculus problems:

: 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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Problem 51: The equation is y 3x + y^3 x + 5 = 0. We need to find (dy)/(dx) using implicit differentiation.

Asked on April 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 21, 2026

Here are the solutions to the calculus problems: Problem 51: The equation is y 3x + y^3 x + 5 = 0. We need to find (dy)/(dx) using implicit differentiation. Step 1: Differentiate both sides of the equation with respect to x. (d)/(dx)(y 3x) + (d)/(dx)(y^3 x) + (d)/(dx)(5) = (d)/(dx)(0) Step 2: Apply the product rule and chain rule for differentiation. For (d)/(dx)(y 3x): dy