Find the implicit derivative $\frac{d}{dx}\left(2\sin\left(x\right)\cos\left(x\right)\right)=1$

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$2\frac{d}{dx}\left(\sin\left(x\right)\cos\left(x\right)\right)=1$

Learn how to solve product rule of differentiation problems step by step online. Find the implicit derivative d/dx(2sin(x)cos(x))=1. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=\cos\left(x\right). 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)}. When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents.