derivative e^{-(x+2)}-sin(x^2)+1

Lösung

ableitung von

e^{- (x + 2)} - sin (x^{2}) + 1

- 2 x cos (x^{2}) - e^{- x - 2}

Schritte zur Lösung

\frac{d}{d x} (e^{- (x + 2)} - sin (x^{2}) + 1)

Vereinfache

e^{- (x + 2)} - sin (x^{2}) + 1 : e^{- x - 2} - sin (x^{2}) + 1

= \frac{d}{d x} (e^{- x - 2} - sin (x^{2}) + 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (e^{- x - 2}) - \frac{d}{d x} (sin (x^{2})) + \frac{d}{d x} (1)

\frac{d}{d x} (e^{- x - 2}) = - e^{- x - 2}

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

\frac{d}{d x} (1) = 0

= - e^{- x - 2} - cos (x^{2}) \cdot 2 x + 0

Vereinfache

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

d er i v a t i v e \frac{x ^{2}}{4} + x + 1

\int \frac{1}{sin ( x ) - 2 csc ( x )} d x

t an g e n t y = \frac{5 x}{x - 2}, (3, 15)

s l o p e f (x) = \frac{x ^{2}}{x + 4}

\int (6 e^{x}) d x