Ask your own question, for FREE!
Mathematics 57 Online
OpenStudy (tad1):

The derivative of an even function is an odd function. The derivative of an odd function is an even function. Prove the results by from the limit definition of the derivative: Lim( as x approaches 0) [f(x - f(a)] / (x - a )

OpenStudy (anonymous):

this is trivial if you get to use the chain rule. but you must use definition yes?

OpenStudy (anonymous):

f(x)'=lim f(x)-f(a)/(x-a) if it is an even function than we know that f(x)=f(-x) f(-x)'=lim f(x)-f(a)/(-x-a)=-f(x)'

OpenStudy (anonymous):

same way if it is odd

OpenStudy (anonymous):

so we assume f is odd and prove f' is even in other word we have to show if \[f(-a)=-f(a)\] then \[f'(-a)=f'(a)\]

OpenStudy (anonymous):

oh what andras said!

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
xXAikoXx: i have hip pain help.
5 minutes ago 2 Replies 1 Medal
alphaXtiger: help .,.
1 hour ago 5 Replies 1 Medal
ihy: here's a song
3 hours ago 0 Replies 0 Medals
ihy: Here's a song I learned.
3 hours ago 0 Replies 0 Medals
abound: Im sad
3 hours ago 6 Replies 1 Medal
xXAikoXx: i got upper back pain help
4 hours ago 9 Replies 2 Medals
Gdub08: What's the best way to study for a test and quiz?
5 hours ago 9 Replies 1 Medal
dkffjlflsjkdfj: find the value of X
7 hours ago 2 Replies 0 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!