SOLUTION: Let {{{ f(t) = (4)/(t^2) }}} Use the defintion of the derivative to determine f'(-1) Let {{{ g(x) = 1/(x+1) }}} Use the defintion of the derivative to determine g'(1) I kno

Algebra ->  Functions -> SOLUTION: Let {{{ f(t) = (4)/(t^2) }}} Use the defintion of the derivative to determine f'(-1) Let {{{ g(x) = 1/(x+1) }}} Use the defintion of the derivative to determine g'(1) I kno      Log On


   

Question 1009038: Let +f%28t%29+=+%284%29%2F%28t%5E2%29+ Use the defintion of the derivative to determine f'(-1)
Let +g%28x%29+=+1%2F%28x%2B1%29+ Use the defintion of the derivative to determine g'(1)

I know that the limit definition of the derivative is lim h->0 +%28f%28x%2Bh%29-f%28x%29%29%2F%28h%29+ just unsure how to apply it exactly.
Please show how this is done
Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28t%29+=+%284%29%2F%28t%5E2%29+ Use the definition of the derivative to determine f'(-1)
+f%28t%29+=+%284%29%2F%28t%5E2%29+=+4t%5E%28-2%29+
f'(t) = -2%2A4t%5E%28-3%29
f'(-1) = -8*(-1)^(-3)
= 8
============
Let +g%28x%29+=+1%2F%28x%2B1%29+ Use the definition of the derivative to determine g'(1)
+g%28x%29+=+1%2F%28x%2B1%29+
+g%28x%29+=+%28x%2B1%29%5E%28-1%29+
g'(x) = -1%2A%28x%2B1%29%5E%28-2%29
g'(-1) = -1%2A2%5E%28-2%29
= -1/4