Friday

February 27, 2015

February 27, 2015

Posted by **nicole** on Wednesday, October 31, 2012 at 11:38am.

first one:

f(t)=2^(log5t)

the 5 is the base

second one:

y=(2(x^2) - 1)^5 /(√(x+1)

for the second one you have to use logarithmic differentiation

- calculus -
**Steve**, Wednesday, October 31, 2012 at 12:19pmrecall that (a^u)' = lna a^u u', so we have

f' = ln2 2^log5t (log5t)'

Now, log5t = lnt/ln5, so

f' = ln2 2^log5t * 1/ln5 * 1/t

f' = ln2/ln5 * 1/t 2^log5t

Now, ln2/ln5 = log5(2), so finally,

f' = (log5(2) / t) 2^log5t

y = u^5/v where

u = 2x^2-1

v = √(x+1)

y' = (5u^4 u' v - u^5 v')/v^2

= u^4 (5vu' - v')/v^2

= (2x^2-1)^4 (5(2x^2-1) - 1/(2√(x+1)))/(x+1)

You can massage this as you want; one form is

(2x^2-1) (38x^2+40x+1)

------------------------------

2(x+1)√(x+1)

- calculus -
**Steve**, Wednesday, October 31, 2012 at 12:20pmoops. forgot an ^4 on the last line

**Answer this Question**

**Related Questions**

calculus - really stuck on these two, steps would be greatly appreciated. gotta ...

Calculus - Determine the intersection, if any, of the planes with equations x + ...

Calculus - Determine the intersection, if any, of the planes with equations x + ...

calculus - okay i need to find the derivative of f(x)=cosπ(x^2) and if you ...

Calculus - R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I ...

Calculus - I need to find the second derivative of y=x(x-1)^1/2. I found the ...

Math - I need someone to check my homework answers. I don't really know this ...

Calculus - y=(√x)/((√x)+1) Find the concavity and point of ...

calculus - okay i need to find the derivative of f(x)=πsin2x and f(x)=cos&#...

Math - What is the first and second derivative of 3/(1+2(x^3)) ? im tempted to ...