What is the derivative of e^xsin(2x+cos(2x)*2e^x) ?

The derivative of e^xsin(2x+cos(2x)*2e^x) is -3e^xsin(2x)+4e^xcos(2x)

What is the first derivative of e^xsin(2x+cos(2x)*2e^x) ?

The first derivative of e^xsin(2x+cos(2x)*2e^x) is -3e^xsin(2x)+4e^xcos(2x)

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\frac{d}{d x} (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x})

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

Solution steps

\frac{d}{d x} (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x})

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x} + 2 (- 2 e^{x} sin (2 x) + e^{x} cos (2 x))

Simplify

e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x} + 2 (- 2 e^{x} sin (2 x) + e^{x} cos (2 x)) : - 3 e^{x} sin (2 x) + 4 e^{x} cos (2 x)

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

x \to 3 lim (25)

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

\int_{0}^{2} (- x^{2} + 2 x) d x

f (x) = 2 x^{- 2}

k = 0 \sum \infty \frac{1}{2 ^{k}}

What is the derivative of e^xsin(2x+cos(2x)*2e^x) ?
The derivative of e^xsin(2x+cos(2x)*2e^x) is -3e^xsin(2x)+4e^xcos(2x)
What is the first derivative of e^xsin(2x+cos(2x)*2e^x) ?
The first derivative of e^xsin(2x+cos(2x)*2e^x) is -3e^xsin(2x)+4e^xcos(2x)