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

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

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

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

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derivative of

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

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

Solution steps

\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)

= \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)

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

Simplify

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)

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

\int \frac{- 5 x ^{2}}{4 x - x ^{2}} d x

f (x) = 8 x^{4} - 3 x^{3} + 4 x

\frac{d}{d x} (cos (sin (x^{4})))

\frac{d}{d y} (y^{1 - n})

\int \frac{2 x ^{2}}{4 + x ^{2}} d x

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