SOLUTION: How do I figure f'(x) & f''(x) from this function.... f(x) = (x+3)^2/3 I have a problem with understanding exponential fractions....

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How do I figure f'(x) & f''(x) from this function.... f(x) = (x+3)^2/3 I have a problem with understanding exponential fractions....      Log On


   

Question 594843: How do I figure f'(x) & f''(x) from this function....
f(x) = (x+3)^2/3
I have a problem with understanding exponential fractions....
Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%282%2C1%2C%22%22%2C%22f%28x%29%22%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2C%28x+%2B+3%29%5E%282%2F3%29%29  Use the rule expr%28d%2F%28dx%29%29u%5En = n%2Au%5E%28n-1%29expr%28%28du%29%2F%28dx%29%29 where u=x%2B3 and n=2%2F3

matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2C2%2F3%29%29matrix%282%2C1%2C%22%22%2C%28x+%2B+3%29%5E%282%2F3-1%29%281%29%29

matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2C2%2F3%29%29matrix%282%2C1%2C%22%22%2C%28x+%2B+3%29%5E%282%2F3-3%2F3%29%281%29%29

matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2C2%2F3%29%29matrix%282%2C1%2C%22%22%2C%28x+%2B+3%29%5E%28-1%2F3%29%29

Use the rule again for %22f%27%27%28x%29%22 with n=-1%2F3

matrix%282%2C1%2C%22%22%2C%22f%27%27%28x%29%22%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2Cexpr%28-1%2F3%29expr%282%2F3%29%29%29matrix%282%2C1%2C%22%22%2C%28x+%2B+3%29%5E%28-1%2F3-1%29%281%29%29

matrix%282%2C1%2C%22%22%2C%22f%27%27%28x%29%22%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2Cexpr%28-1%2F3%29expr%282%2F3%29%29%29matrix%282%2C1%2C%22%22%2C%28x+%2B+3%29%5E%28-1%2F3-3%2F3%29%281%29%29

matrix%282%2C1%2C%22%22%2C%22f%27%27%28x%29%22%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2C-2%2F9%29%29matrix%282%2C1%2C%22%22%2C%28x+%2B+3%29%5E%28-4%2F3%29%29

Edwin