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Popular >

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

Solution

derivative of

sin (2 x) cos (3 x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral of x^2e^xcos(x)

\int x^{2} e^{x} cos (x) d x

integral of 2xcos(x^2)

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

area f(x)=0.2x^2+10,g(x)=x,x=-7,x=2 area

f (x) = 0.2 x^{2} + 10, g (x) = x, x = - 7, x = 2

(\partial)/(\partial x)(ln(8x^2+9y^2))

\frac{\partial}{\partial x} (ln (8 x^{2} + 9 y^{2}))

integral from-1 to 2 of (3x^2-2x+3)

\int_{- 1}^{2} (3 x^{2} - 2 x + 3) d x

Frequently Asked Questions (FAQ)

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