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Popular >

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

Solution

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

Solution

- 2 e^{x} sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of 3.5+5.6

x \to 2 lim (3.5 + 5.6)

limit as x approaches 2-of (2-|x|)/(2+x)

x \to 2 - lim (\frac{2 - ∣ x ∣}{2 + x})

derivative of (4x+3)^5 derivative of

(4 x + 3)^{5}

y^{''}-3y^'-4y=6e^{2t}

y^{^{''}} - 3 y^{^{'}} - 4 y = 6 e^{2 t}

(\partial)/(\partial x)(e^{-(x^2+y^2+z^2)})

\frac{\partial}{\partial x} (e^{- (x^{2} + y^{2} + z^{2})})

Frequently Asked Questions (FAQ)

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