Question

Logarithmische Ableitung:

f(x)=x^{sin'x'+7}

Answer 1

f(x) = x^ (SIN(x) + 7)

f(x) = EXP(LN(x^ (SIN(x) + 7)))

f(x) = EXP((SIN(x) + 7)·LN(x))

f'(x) = EXP((SIN(x) + 7)·LN(x)) · ((COS(x) + 7)·LN(x) + (SIN(x) + 7)·1/x)

f'(x) = x^{SIN(x) + 7} · (COS(x)·LN(x) + (SIN(x) + 7)·1/x)

f'(x) = x^{SIN(x) + 6} · (x·COS(x)·LN(x) + SIN(x) + 7)

Answer 2