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

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

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

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

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

- 2 e^{x} sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

y^{^{''}} + 36 y^{^{'}} = 0

x \to \frac{π}{2} + lim (sec (x))

\int x (9 - x^{2}) d x

f (x) = \frac{5 x}{x + 2}, (3, 3)

\int_{0}^{4} \frac{x}{8} d x

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