What is the derivative of cos(2xsin(3x)) ?

The derivative of cos(2xsin(3x)) is -2sin(2x)sin(3x)+3cos(3x)cos(2x)

What is the first derivative of cos(2xsin(3x)) ?

The first derivative of cos(2xsin(3x)) is -2sin(2x)sin(3x)+3cos(3x)cos(2x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int (7 x^{6} - \frac{6}{x ^{6}}) d x

\int x^{2} - 3 x + 8 d x

(- 7, - 6), (10, 8)

(3 x - 10)^{\frac{4}{3}}

\frac{\partial}{\partial x} (1 + x^{4} + y^{4})

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