Find dy/dx for the equation sin(x2y3) + 3x2y2 = 6 using implicit differentiation.

April 13, 2026Mathematics

ScanSolve AI Answer

April 13, 2026

Answer

6$:

To find $\frac{dy}{dx}$ using implicit differentiation for the equation $\sin(x^2y^3) + 3x^2y^2 = 6$ :

Step 1: Differentiate both sides of the equation with respect to $x$ . $\frac{d}{dx}[\sin(x^2y^3) + 3x^2y^2] = \frac{d}{dx}[6]$

Step 2: Apply the chain rule and product rule to differentiate each term. For the first term, $\frac{d}{dx}[\sin(x^2y^3)]$ : Let $u = x^2y^3$ . Then $\frac{d}{dx}[\sin(u)] = \cos

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To find (dy)/(dx) using implicit differentiation for the equation (x^2y^3) + 3x^2y^2 = 6: Step 1: Differentiate both sides of the equation with respect to x.

Asked on April 13, 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 13, 2026

To find (dy)/(dx) using implicit differentiation for the equation (x^2y^3) + 3x^2y^2 = 6: Step 1: Differentiate both sides of the equation with respect to x. (d)/(dx)[(x^2y^3) + 3x^2y^2] = (d)/(dx)[6] Step 2: Apply the chain rule and product rule to differentiate each term. For the first term, (d)/(dx)[(x^2y^3)]: Let u = x^2y^3. Then $(d)/(dx)[(u)] =