Ableitungen bestimmen: f(x) = 3ex · sin(x2)

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(x²)

f'(x) = 3·e^x·SIN(x²) + 3·e^x·COS(x²)·2·x)

f'(x) = 3·e^x·(2·x·COS(x²) + SIN(x²))

f(x) = 3·e^x·(SIN(x²) + 2·x·COS(x²))

f'(x) = 3·e^x·(SIN(x²) + 2·x·COS(x²)) + 3·e^x·(SIN(x²)·2·x + (2·COS(x²) - (2·x)²·SIN(x²)))

f'(x) = 3·e^x·((4·x + 2)·COS(x²) + (1 - 4·x²)·SIN(x²))