What is the derivative of 2(e^xcos(x-e^xsin(x))) ?

The derivative of 2(e^xcos(x-e^xsin(x))) is -4e^xsin(x)

What is the first derivative of 2(e^xcos(x-e^xsin(x))) ?

The first derivative of 2(e^xcos(x-e^xsin(x))) is -4e^xsin(x)

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

- 4 e^{x} sin (x)

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= - 4 e^{x} sin (x)

f (x) = \frac{1}{2} x - \frac{1}{10}

f (x) = \frac{4}{3} π x^{3}

k = 5 \sum \infty \frac{k + 7}{k + 6}

\frac{d}{d x} (\frac{tan ( x ) - 3}{sec ( x )})

f (x) = 7 x

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