What is the derivative of sin(2xcos(3x)) ?

The derivative of sin(2xcos(3x)) is 2cos(2x)cos(3x)-3sin(3x)sin(2x)

What is the first derivative of sin(2xcos(3x)) ?

The first derivative of sin(2xcos(3x)) is 2cos(2x)cos(3x)-3sin(3x)sin(2x)

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\frac{d}{d x} (sin (2 x) cos (3 x))

2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)

Solution steps

\frac{d}{d x} (sin (2 x) cos (3 x))

Apply the Product Rule:

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

f = sin (2 x), g = cos (3 x)

= \frac{d}{d x} (sin (2 x)) cos (3 x) + \frac{d}{d x} (cos (3 x)) sin (2 x)

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= cos (2 x) \cdot 2 cos (3 x) + (- sin (3 x) \cdot 3) sin (2 x)

Simplify

= 2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)

What is the derivative of sin(2xcos(3x)) ?
The derivative of sin(2xcos(3x)) is 2cos(2x)cos(3x)-3sin(3x)sin(2x)
What is the first derivative of sin(2xcos(3x)) ?
The first derivative of sin(2xcos(3x)) is 2cos(2x)cos(3x)-3sin(3x)sin(2x)