What is the (cos(x)sin(x))^' ?

The (cos(x)sin(x))^' is cos(2x)

What is the first (cos(x)sin(x))^' ?

The first (cos(x)sin(x))^' is cos(2x)

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(cos (x) sin (x))^{^{'}}

cos (2 x)

Solution steps

(cos (x) sin (x))^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = sin (x)

= (cos (x))^{^{'}} sin (x) + (sin (x))^{^{'}} cos (x)

(cos (x))^{'} = - sin (x)

(sin (x))^{'} = cos (x)

= (- sin (x)) sin (x) + cos (x) cos (x)

Simplify

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

\frac{\partial}{\partial x} (3 x e^{- x y})

e^{- 2 s} \frac{1}{10 s + 2}

\frac{d}{d x} (2 x^{\frac{3}{2}} + 7)

\int \frac{( ln ( x ) ) ^{11}}{x} d x

(arctan (x))^{^{'}}