What is the derivative of 6e^{3x}(3cos(4x)-4sin(4x)) ?

The derivative of 6e^{3x}(3cos(4x)-4sin(4x)) is 6(-7e^{3x}cos(4x)-24e^{3x}sin(4x))

What is the first derivative of 6e^{3x}(3cos(4x)-4sin(4x)) ?

The first derivative of 6e^{3x}(3cos(4x)-4sin(4x)) is 6(-7e^{3x}cos(4x)-24e^{3x}sin(4x))

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derivative of

6 e^{3 x} (3 cos (4 x) - 4 sin (4 x))

6 (- 7 e^{3 x} cos (4 x) - 24 e^{3 x} sin (4 x))

Solution steps

\frac{d}{d x} (6 e^{3 x} (3 cos (4 x) - 4 sin (4 x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (e^{3 x} (3 cos (4 x) - 4 sin (4 x)))

Apply the Product Rule:

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

f = e^{3 x}, g = 3 cos (4 x) - 4 sin (4 x)

= 6 (\frac{d}{d x} (e^{3 x}) (3 cos (4 x) - 4 sin (4 x)) + \frac{d}{d x} (3 cos (4 x) - 4 sin (4 x)) e^{3 x})

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (3 cos (4 x) - 4 sin (4 x)) = - 12 sin (4 x) - 16 cos (4 x)

= 6 (e^{3 x} \cdot 3 (3 cos (4 x) - 4 sin (4 x)) + (- 12 sin (4 x) - 16 cos (4 x)) e^{3 x})

Expand

e^{3 x} \cdot 3 (3 cos (4 x) - 4 sin (4 x)) + (- 12 sin (4 x) - 16 cos (4 x)) e^{3 x} : - 7 e^{3 x} cos (4 x) - 24 e^{3 x} sin (4 x)

= 6 (- 7 e^{3 x} cos (4 x) - 24 e^{3 x} sin (4 x))

What is the derivative of 6e^{3x}(3cos(4x)-4sin(4x)) ?
The derivative of 6e^{3x}(3cos(4x)-4sin(4x)) is 6(-7e^{3x}cos(4x)-24e^{3x}sin(4x))
What is the first derivative of 6e^{3x}(3cos(4x)-4sin(4x)) ?
The first derivative of 6e^{3x}(3cos(4x)-4sin(4x)) is 6(-7e^{3x}cos(4x)-24e^{3x}sin(4x))