You need to determine the first derivative of this function.

You should notice that f(x) is the product of two trigonometric functions, sin x and cos x, hence you need to use the product rule to evaluate the first derivative.

Applying the product rule yields:

`f'(x) = 6(cos x)'*(sin x) +...

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You need to determine the first derivative of this function.

You should notice that f(x) is the product of two trigonometric functions, sin x and cos x, hence you need to use the product rule to evaluate the first derivative.

Applying the product rule yields:

`f'(x) = 6(cos x)'*(sin x) + 6(cos x)*(sin x)'`

`f'(x) = 6 (- sinx)*(sin x) + 6 (cos x)*(cos x)`

`f'(x) = 6(cos^2 x - sin^2 x)`

Notice that the difference of squares in the brackets yields the cosine of double of the argument x.

f'(x) = `6 cos 2x`

**Evaluating the first derivative of the function f(x) = 6 sin x*cos x yields: f'(x) = `6 cos 2x` .**