derivative of e^x(cos(x-sin(x)))

Lösung

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

- 2 e^{x} sin (x)

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (x) - sin (x)

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Vereinfache

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

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

y^{^{'}} = sin^{2} (x - y)

\frac{d}{d x} (\frac{3 x - 4}{12 x ^{2}})

s l o p e F (x) = x + 1

y^{^{'}} = \frac{( x ^{2} - y ^{2} )}{x y}, y (2) = 2

d er i v a t i v e cos^{4} (x)