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

Lösung

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

2 e^{x} sin (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 2 e^{x} sin (x)

a re a x^{2}, 12 - x, - 4, 3

\int (- x^{4} + 1)^{2} (- 4 x^{3}) d x

\frac{d}{d x} (\frac{8 x ^{3} - 6}{x ^{2}})

y^{^{'}} = - x

d er i v a t i v e y = (\frac{x ^{2} + 6}{x ^{2} - 6})^{3}