What is the derivative of 2sin(2x-2cos(2x)-1/5 e^x) ?

The derivative of 2sin(2x-2cos(2x)-1/5 e^x) is 4cos(2x)+4sin(2x)-1/5 e^x

What is the first derivative of 2sin(2x-2cos(2x)-1/5 e^x) ?

The first derivative of 2sin(2x-2cos(2x)-1/5 e^x) is 4cos(2x)+4sin(2x)-1/5 e^x

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\frac{d}{d x} (2 sin (2 x) - 2 cos (2 x) - \frac{1}{5} e^{x})

4 cos (2 x) + 4 sin (2 x) - \frac{1}{5} e^{x}

Solution steps

\frac{d}{d x} (2 sin (2 x) - 2 cos (2 x) - \frac{1}{5} e^{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 sin (2 x)) - \frac{d}{d x} (2 cos (2 x)) - \frac{d}{d x} (\frac{1}{5} e^{x})

\frac{d}{d x} (2 sin (2 x)) = 4 cos (2 x)

\frac{d}{d x} (2 cos (2 x)) = - 4 sin (2 x)

\frac{d}{d x} (\frac{1}{5} e^{x}) = \frac{1}{5} e^{x}

= 4 cos (2 x) - (- 4 sin (2 x)) - \frac{1}{5} e^{x}

Simplify

= 4 cos (2 x) + 4 sin (2 x) - \frac{1}{5} e^{x}

What is the derivative of 2sin(2x-2cos(2x)-1/5 e^x) ?
The derivative of 2sin(2x-2cos(2x)-1/5 e^x) is 4cos(2x)+4sin(2x)-1/5 e^x
What is the first derivative of 2sin(2x-2cos(2x)-1/5 e^x) ?
The first derivative of 2sin(2x-2cos(2x)-1/5 e^x) is 4cos(2x)+4sin(2x)-1/5 e^x