Step-by-step Solution

Find the derivative using the product rule $\frac{d}{dx}\left(4\sin\left(x\right)\cos\left(x\right)\right)$

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(4\sin\left(x\right)\cdot \cos\left(x\right)\right)$

Learn how to solve product rule of differentiation problems step by step online.

$4\frac{d}{dx}\left(\sin\left(x\right)\cos\left(x\right)\right)$

Unlock this full step-by-step solution!

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(4sin(x)*cos(x)). The derivative of a function multiplied by a constant (4) 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)}. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).

Final Answer

$4\left(\cos\left(x\right)^2-\sin\left(x\right)^2\right)$
$\frac{d}{dx}\left(4\sin\left(x\right)\cdot \cos\left(x\right)\right)$

Related formulas:

4. See formulas

Time to solve it:

~ 0.04 s (SnapXam)