What is the derivative of sin(6xcos(4x)) ?

The derivative of sin(6xcos(4x)) is 6cos(6x)cos(4x)-4sin(4x)sin(6x)

What is the first derivative of sin(6xcos(4x)) ?

The first derivative of sin(6xcos(4x)) is 6cos(6x)cos(4x)-4sin(4x)sin(6x)

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\frac{d}{d x} (sin (6 x) cos (4 x))

6 cos (6 x) cos (4 x) - 4 sin (4 x) sin (6 x)

Solution steps

\frac{d}{d x} (sin (6 x) cos (4 x))

Apply the Product Rule:

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

f = sin (6 x), g = cos (4 x)

= \frac{d}{d x} (sin (6 x)) cos (4 x) + \frac{d}{d x} (cos (4 x)) sin (6 x)

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= cos (6 x) \cdot 6 cos (4 x) + (- sin (4 x) \cdot 4) sin (6 x)

Simplify

= 6 cos (6 x) cos (4 x) - 4 sin (4 x) sin (6 x)

What is the derivative of sin(6xcos(4x)) ?
The derivative of sin(6xcos(4x)) is 6cos(6x)cos(4x)-4sin(4x)sin(6x)
What is the first derivative of sin(6xcos(4x)) ?
The first derivative of sin(6xcos(4x)) is 6cos(6x)cos(4x)-4sin(4x)sin(6x)