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

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

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

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

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derivative of

sin (3 x) cos (2 x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int sin^{4} (2 x) cos^{2} (2 x) d x

\int 3 sin (5 x) d x

\int \frac{1}{1 + x ^{\frac{3}{2}}} d x

\frac{d}{d t} (\frac{tan ( t )}{cos ( t ) - 4})

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

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