SOLUTION: Find the derivative of the function y=ln(2x^5) Show all steps worked out

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the derivative of the function y=ln(2x^5) Show all steps worked out      Log On


   

Question 541814: Find the derivative of the function y=ln(2x^5) Show all steps worked out
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
We know that %28d%2Fdx%29ln%28x%29=%281%2Fx%29dx
So use a plug. Instead of 2x%5E5, use "u"
%28d%2Fdu%29ln%28u%29=%281%2Fu%29%28du%29
u=2x%5E5
du=10x%5E%284%29dx
So
Therefore, %28dy%2Fdx%29ln%282x%5E5%29=%285%2Fx%29dx
.
.
.
That shows you how's it's done. The super easy way from here on out, just learn that %28d%2Fdx%29ln%28c%2Ax%5En%29=%28n%2Fx%29dx
"C" = any constant, and is irrelevant. Just put the exponent over x and you're done! :-)
Hope this helps!