Ableitungen bestimmen: f(x) = 3e^x · sin(x^2)

Question

Ableitungen bestimmen:

a) \( f(x)=3 e^{x} \cdot \sin \left(x^{2}\right) \)

b) \( f(x)=3 e^{x}\left(\sin \left(x^{2}\right)+2 x \cdot \cos \left(x^{2}\right)\right) \)

Answer 1

f(x) = 3·e^x·SIN(x^2)

f'(x) = 3·e^x·SIN(x^2) + 3·e^x·COS(x^2)·2·x)

f'(x) = 3·e^x·(2·x·COS(x^2) + SIN(x^2))

f(x) = 3·e^x·(SIN(x^2) + 2·x·COS(x^2))

f'(x) = 3·e^x·(SIN(x^2) + 2·x·COS(x^2)) + 3·e^x·(SIN(x^2)·2·x + (2·COS(x^2) - (2·x)^2·SIN(x^2)))

f'(x) = 3·e^x·((4·x + 2)·COS(x^2) + (1 - 4·x^2)·SIN(x^2))