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Popular >

derivative of sin(3xcos(2x))

Solution

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

Solution

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)

Popular Examples

integral of 1/(x^3-1)

\int \frac{1}{x ^{3} - 1} d x

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\frac{d y}{d x}, x^{2} - y^{3} = 6

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\int cos (x) + \frac{1}{3} sin (x) - \frac{1}{x ^{2}} d x

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\int_{0}^{2} e^{2 x} d x

derivative of (2^{x+1}-3.5^x^3)

\frac{d}{d x} ((2^{x + 1} - 3. 5^{x})^{3})

Frequently Asked Questions (FAQ)

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