composition of function

[Scorpy]

If g(0)=f(1)=0 and g'(1)=f'(0)=1 then how to find the derivative of sin(f(e^g(x))) for x=pi/2. Someone to help me??

 

[pka]

If g(0)=f(1)=0 and g'(1)=f'(0)=1 then how to find the derivative of sin(f(e^g(x))) for x=pi/2. Someone to help me??

There appears to be a mistake in the statement of the question.
The derivative is \(\displaystyle \cos \left( {f\left( {{e^{g(x)}}} \right)} \right)f'\left( {{e^{g(x)}}} \right)g'\left( x \right){e^{g(x)}}\)

The difficulty is that we do not know what \(\displaystyle g\left(\frac{\pi}{2}\right)\) equals.
If it were at \(\displaystyle x=0\), then it is doable.

 

[Scorpy]

I was not sure if it was pi/2, I couldn't remember So it must be 0.
Thanks anyway, now it's much clear to me