Find the implicit derivative $\frac{d}{dy}\left(y+x=\sin\left(xy^2\right)\right)$

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$\frac{d}{dy}\left(y+x\right)=\frac{d}{dy}\left(\sin\left(xy^2\right)\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dy(y+x=sin(xy^2)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=y^2. The derivative of the linear function is equal to 1.