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- Find the derivative using the definition
- Exact Differential Equation
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- Find the derivative using the product rule
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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 ${f'(x) = \cos(x)\cdot D_x(x)}$
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$\frac{d}{dx}\left(x+y\right)\cos\left(x+y\right)=6x-6y$
Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(sin(x+y))=6x-6y. 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 a sum of two or more functions is the sum of the derivatives of each function. Divide both sides of the equation by \cos\left(x+y\right). Group the terms of the equation by moving the terms that have the variable y^{\prime} to the left side, and those that do not have it to the right side.