What is the derivative of sin(x)*cos(x) ?

The derivative of sin(x)*cos(x) is cos(2x)

What is the first derivative of sin(x)*cos(x) ?

The first derivative of sin(x)*cos(x) is cos(2x)

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derivative of

sin (x) \cdot cos (x)

cos (2 x)

Solution steps

\frac{d}{d x} (sin (x) cos (x))

Apply the Product Rule:

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

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

= \frac{d}{d x} (sin (x)) cos (x) + \frac{d}{d x} (cos (x)) sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

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

= cos (2 x)

What is the derivative of sin(x)*cos(x) ?
The derivative of sin(x)*cos(x) is cos(2x)
What is the first derivative of sin(x)*cos(x) ?
The first derivative of sin(x)*cos(x) is cos(2x)