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Find dy/dx for sin(x2y3) + 3x3y2 = 6 using implicit differentiation.

April 13, 2026Mathematics

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To find $\frac{dy}{dx}$ for the given equation $\sin(x^2y^3) + 3x^3y^2 = 6$ , we use implicit differentiation. Your initial steps are correct, but there are some sign errors and factorization issues in the later steps.

Differentiate both sides of the equation with respect to $x$ .
$\frac{d}{dx}(\sin(x^2y^3)) + \frac{d}{dx}(3x^3y^2) = \frac{d}{dx}(6)$
Differentiate the first term, $\sin(x^2y^3)$ , using the chain rule.
Let $u = x^2y^3$ . Then

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Find dy/dx for sin(x2y3) + 3x3y2 = 6 using implicit differentiation.

Step-by-step solution

Differentiate both sides of the equation with respect to xxx.

Differentiate the first term, sin⁡(x2y3)\sin(x^2y^3)sin(x2y3), using the chain rule.

Still stuck on this one?

More Mathematics Questions

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

Differentiate the first term, $\sin(x^2y^3)$ , using the chain rule.