What is the derivative of 7(e^xcos(x-e^xsin(x))) ?

The derivative of 7(e^xcos(x-e^xsin(x))) is -14e^xsin(x)

What is the first derivative of 7(e^xcos(x-e^xsin(x))) ?

The first derivative of 7(e^xcos(x-e^xsin(x))) is -14e^xsin(x)

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\frac{d}{d x} (7 (e^{x} cos (x) - e^{x} sin (x)))

- 14 e^{x} sin (x)

Solution steps

\frac{d}{d x} (7 (e^{x} cos (x) - e^{x} sin (x)))

Take the constant out:

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

= 7 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Apply the Sum/Difference Rule:

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

= 7 (\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}

= 7 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x}))

Simplify

7 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 14 e^{x} sin (x)

= - 14 e^{x} sin (x)

What is the derivative of 7(e^xcos(x-e^xsin(x))) ?
The derivative of 7(e^xcos(x-e^xsin(x))) is -14e^xsin(x)
What is the first derivative of 7(e^xcos(x-e^xsin(x))) ?
The first derivative of 7(e^xcos(x-e^xsin(x))) is -14e^xsin(x)