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- Find the derivative using the definition
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sin\left(x\right)$ and $g=y$
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$y\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(y\right)\sin\left(x\right)=3$
Learn how to solve problems step by step online. Find the implicit derivative d/dx(sin(x)y)=3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=y. The derivative of the linear function is equal to 1. 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)}. The derivative of the linear function is equal to 1.