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

April 13, 2026Mathematics

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

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