Well, say you have y=a^x, Take logs of both sides, lny=ln(a^x)=xlna then y=e^(xlna)=a^x Then differentiate that normally, i.e. f'(x)e^[f(x)] then y'=lna.e^(xlna)=lna.a^x
Well, say you have y=a^x, Take logs of both sides, lny=ln(a^x)=xlna then y=e^(xlna)=a^x Then differentiate that normally, i.e. f'(x)e^[f(x)] then y'=lna.e^(xlna)=lna.a^x
So you've said that the differential of xlna is lna (which is what you multiply e^xlna by), whereas product rule says that the differential of xlna is x/a + lna? Not sure I've followed you. How does xlna differentiate to lna?
So you've said that the differential of xlna is lna (which is what you multiply e^xlna by), whereas product rule says that the differential of xlna is x/a + lna? Not sure I've followed you. How does xlna differentiate to lna?
a is a constant, therefore so is lna, so product rule would yield lna.dx/dx + x.d(lna)/dx = lna + 0