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Popular >

derivative of e^xcos(x-e^xsin(x))

Solution

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

Solution

- 2 e^{x} sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

= \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}

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

Simplify

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

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

Popular Examples

derivative of (sin(x/4+cos(x))^{1/x})

\frac{d}{d x} ((sin (\frac{x}{4}) + cos (x))^{\frac{1}{x}})

(1x+ye^{y/x})dx-xe^{y/x}dy=0

(1 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

limit as x approaches 8+of 3/(x-8)

x \to 8 + lim (\frac{3}{x - 8})

integral of ln((7x)^2)

\int ln ((7 x)^{2}) d x

(\partial)/(\partial x)(cos(2x+4y))

\frac{\partial}{\partial x} (cos (2 x + 4 y))

Frequently Asked Questions (FAQ)

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