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

The derivative of e^{3x}cos(x+e^{3x}sin(x)) is 4e^{3x}cos(x)+2e^{3x}sin(x)

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

The first derivative of e^{3x}cos(x+e^{3x}sin(x)) is 4e^{3x}cos(x)+2e^{3x}sin(x)

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\frac{d}{d x} (e^{3 x} cos (x) + e^{3 x} sin (x))

4 e^{3 x} cos (x) + 2 e^{3 x} sin (x)

Solution steps

\frac{d}{d x} (e^{3 x} cos (x) + e^{3 x} sin (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= 4 e^{3 x} cos (x) + 2 e^{3 x} sin (x)

\int x^{3} e^{- x^{2}} d x

x \to + 2 lim (3 x^{2} + 4 x - 3)

y = - x^{2} + 2 x + 5, y = \frac{x ^{2}}{2} - 4 x + 5

x \to 0 lim (ln (1 + \frac{1}{x}))

\int e^{- 7 t} d t

What is the derivative of e^{3x}cos(x+e^{3x}sin(x)) ?
The derivative of e^{3x}cos(x+e^{3x}sin(x)) is 4e^{3x}cos(x)+2e^{3x}sin(x)
What is the first derivative of e^{3x}cos(x+e^{3x}sin(x)) ?
The first derivative of e^{3x}cos(x+e^{3x}sin(x)) is 4e^{3x}cos(x)+2e^{3x}sin(x)