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Popular >

derivative of cos(3xcos(2x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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\frac{d}{d x} (lo g_{5} (2 x - 5))

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Frequently Asked Questions (FAQ)

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