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Popular Calculus >

derivative of cos(3t)sin(2t)

Solution

derivative of

cos (3 t) sin (2 t)

Solution

- 3 sin (3 t) sin (2 t) + 2 cos (2 t) cos (3 t)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= - 3 sin (3 t) sin (2 t) + 2 cos (2 t) cos (3 t)

Graph

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\int \frac{6}{sin ^{2} ( x )} d x

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\int \frac{2 x + 5}{9 - x ^{2}} d x

Frequently Asked Questions (FAQ)

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