Derivatives of Composite Functions

[Dough]

I just need a nudge in the rigth direction ais don't know where to start
Let y = f(x^2 + 3x - 5) find dy/dx when x = 1, given that f'(-1) = 2

Thanks!

 

[AKG]

Let g(x) = x² + 3x - 5, then y = f(g(x)). dy/dx = f'(g(x))g'(x)

 

[Dough]

i am not sure what else y have to do to get the answer, i wrote that out as well as

-1 = x^2 + 3x -5
solved and got x = 1 or -3...

but what else?

dy/dx = f'(x^2 + 3x - 5)(2x + 3)

 

[HallsofIvy]

i am not sure what else y have to do to get the answer, i wrote that out as well as
-1 = x^2 + 3x -5
solved and got x = 1 or -3...
but what else?
dy/dx = f'(x^2 + 3x - 5)(2x + 3)

I suggest going back and reading the problem again! You were asked to find y'(1). How about setting x= 1?

 

[Jameson]

Very good suggestion.

And just to ease your worries, you were given a good piece of information: that f'(-1)=2. Do you see where this applies to the problem?