Solving for g|(-1): Finding the Answer

[Dell]

any ideas??

given:
y=f(x)
f^|(1)=4
g(x)=f(x²)

find g^|(-1)
------------------------------------

i know that g(-1)=g(1) because g is a squared function of x, but that's about it,
can i say-

g^|(x)=[f(x²)]^|=f^|(x²)*(2x)

and because x=-1, and -1²=1, and i know f^|(1)=4
so
g^|(-1)=-8

 

[nrqed]

given:
y=f(x)
f^|(1)=4
g(x)=f(x²)

find g^|(-1)
------------------------------------

i know that g(-1)=g(1) because g is a squared function of x, but that's about it,
can i say-

g^|(x)=[f(x²)]^|=f^|(x²)*(2x)

and because x=-1, and -1²=1, and i know f^|(1)=4
so
g^|(-1)=-8

Yes, this is exactly right. Good job.

 

[HallsofIvy]

Yes, that's exactly right. Although you would be better advised to use ', a single apostrophe to indicate the derivative rather than |.

 

[Dell]

thanks, is there any way i would be able to solve it if i weren't given 1 as my x?