Thursday

August 28, 2014

August 28, 2014

Posted by **Kristina** on Wednesday, November 17, 2010 at 11:07am.

- CALC -
**Reiny**, Wednesday, November 17, 2010 at 11:29amThere are certain pattern that you should recognize in derivatives

e.g. if y = ln(anything)

then dy/dx = derivative(anything)/anything

I noticed that the derivative of the denominator appears at the top, differing only in a constant

so let's start with

y = ln(1 + 4e^(2t))

dy/dt = 8e^(2t)/(1 + 4e^(2t) )

instead of the 5 I need on top I see an 8

so how about

y = (5/8)ln(1 + 4e^(2t) ) + C

**Related Questions**

Calculus - Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I ...

Calculus - Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I ...

calc - find integral using table of integrals ) integral sin^4xdx this the ...

calc asap! - can you help me get started on this integral by parts? 4 S sqrt(t) ...

CALC - Evaluate The integral from 0 to 5 of (t)(e^-t)dt. I got -5e^-5+-e^-5, but...

calc - how do you start this problem: integral of xe^(-2x) There are two ways: 1...

Calculus 2 - The question is: Evaluate the improper integral for a>0. The ...

Calc - Evaluate the integral using any method: (Integral)sec^3x/tanx dx I ...

Calculus integral - evaluate the integral: integral from -pi/4 to 0 for the ...

Calc 121 - How do you integrate using substitution: the integral from 1 to 3 of...