Final Answer
Step-by-step Solution
Problem to solve:
Specify the solving method
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 $g=\cos\left(x\right)$
Learn how to solve differential calculus problems step by step online.
$4\frac{d}{dx}\left(\sin\left(x\right)\cos\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 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).