derivative y=e^{in(x^2+1)}

Lösung

ableitung von

y = e^{in (x^{2} + 1)}

- sin (n x^{2} + n) \cdot 2 n x + i cos (n x^{2} + n) \cdot 2 n x

Schritte zur Lösung

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

Vereinfache

e^{in (x^{2} + 1)} : cos (n x^{2} + n) + i sin (n x^{2} + n)

= \frac{d}{d x} (cos (n x^{2} + n) + i sin (n x^{2} + n))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (cos (n x^{2} + n)) + \frac{d}{d x} (i sin (n x^{2} + n))

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

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

= - sin (n x^{2} + n) \cdot 2 n x + i cos (n x^{2} + n) \cdot 2 n x

x \to 2 lim (\frac{3 3 x ^{2} - 2 x - 8}{( x + 2 ) ^{3}})

t a y l or \frac{1}{( 1 + x ^{2} )}

\int \frac{x ^{2}}{9 - x ^{2}} d x

\frac{d}{d x} (ln (sin (3^{x^{2}})))

(x^{2} + y^{2}) d x - 2 x y d y = 0