find g'(2) if g(x)=x^3h(cos(pi*x)), where h(1) = 2 h'(1)=-2
im really stuck on this one and frankly don't even know where to start
thanks so much
The standard method to find the derivative of functions of type where and are functions of is by taking logarithm on both sides and proceeding.
On the right side you have this very occurrence. Here, while .
Let's take log both sides and proceed...
.
Differentiating w.r.t. throughout...
In your original equation if we put x=2,
which is not so we can put in the eqn 2 abv.
Which if we do, the right side of eqn 2 takes the value 1/2.
So, we have, .
So, you can find , now
I thought the problem was while it is actually:
Better if you had used Latex or I had interpreted you better.
Anyway,
you can simply differentiate that equation w.r.t. x throughout and put x=2 in the equation that follows.
Let's do that...
In the equation and the equation above we put and get
OK, now?
thank you very much, it was actually a simple problem :S just that h(1)=2 confused me but now i understand.. thank you
oh by the way my final answer was g'(2)=8 is that correct?
also sorry about not using latex when i have some more time ill figure it out
thanks again