1. Differentiate (x^2+1)^sinx

f(x)=(x^2+1)^sinx
f'(x)=?

I know how to apply the chain rule, so my question really is how do I differentiate u^sinx?

Thanks, feyomi.

2. By using the logarithmic differentiation.
Do you know it ?
If no, Where did you see this problem ?
Or is it from your mind ?

3. Originally Posted by General
By using the logarithmic differentiation.
Do you know it ?
If no, Where did you see this problem ?
Or is it from your mind ?
It's been a while since I've had to solve anything this way, I can't remember..
This is a problem on a past exam paper for Level One Calculus for Uni.
I have an exam on 20th, I've solved everything on the paper except this.

4. Originally Posted by feyomi
It's been a while since I've had to solve anything this way, I can't remember..
This is a problem on a past exam paper for Level One Calculus for Uni.
I have an exam on 20th, I've solved everything on the paper except this.
Let $\displaystyle y=(x^2+1)^{sinx}$
take the natural logarithmic of both sides.
$\displaystyle ln(y) = (sinx) ln(x^2+1)$
Now differentiate both sides with respect to x.

5. Right gotcha.
If y = ln(x)
Does y' = 1/x ?
I can solve it now (if I remembered that right)
Thanks

6. Originally Posted by feyomi
Right gotcha.
If y = ln(x)
Does y' = 1/x ?
I can solve it now (if I remembered that right)
Thanks
Yes. You are correct.