calculus
posted by nicole .
really stuck on these two, steps would be greatly appreciated. gotta find the derivative thanks!
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

recall 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^21
v = √(x+1)
y' = (5u^4 u' v  u^5 v')/v^2
= u^4 (5vu'  v')/v^2
= (2x^21)^4 (5(2x^21)  1/(2√(x+1)))/(x+1)
You can massage this as you want; one form is
(2x^21) (38x^2+40x+1)

2(x+1)√(x+1) 
oops. forgot an ^4 on the last line
Respond to this Question
Similar Questions

Calculus
R=M^2(c/2m/3) dR/dM=CMM^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? 
Math
I need someone to check my homework answers. I don't really know this stuff but i'm trying to do better in math this year. I didn't understand how to do some either. 1. √12 I got 2√3 2. √9a^3 I got 3a 3. √8 … 
Calculus
I need to find the second derivative of y=x(x1)^1/2. I found the first derivative is 2x1/2(x1)^1/2, if someone could check, but I am miserably stuck on the second derivative. 
calculus
really stuck on these two, steps would be greatly appreciated. gotta find the derivative thanks! first one: f(t)=2^(log5t) the 5 is the base second one: y=(2(x^2)  1)^5 /(√(x+1) 
calculus
okay i need to find the derivative of f(x)=cosπ(x^2) and if you could show steps it would be GREATLY appreciated. thank you so much! 
Calculus
Determine the intersection, if any, of the planes with equations x + y  z + 12 = 0 and 2x + 4y  3z + 8 = 0. I have no clue where to even begin. If someone could help and give me the steps to complete it, that would be greatly appreciated. … 
Calculus
Determine the intersection, if any, of the planes with equations x + y  z + 12 = 0 and 2x + 4y  3z + 8 = 0. I have no clue where to even begin. If someone could help and give me the steps to complete it, that would be greatly appreciated. … 
Calculus
How would I find the second derivative if f(x)= √(x^3+2) using the quotient rule. I got to the step where [(12x√(x^3+2))(9x^4/√(x^3+2))]/4(x^3+2) how would i go from that to: (3x(x^3+8))/(4(x^3+2)^3/2) 
Math
Could I please get some help for these 3 questions, apologies for asking so many, but they were the ones I was really unsure of: 1. Find an equation for the line tangent to y=ln(x) and that goes through the origin. I have no idea, … 
Multivariable calculus
Hello, I have the next exercise about chain rule in multivariable calculus: I have to show that the differential equation: y(dz/dx)x(dz/dy) = (yx)z can be change to the equation: (dw/dv) = 0 using the new variables: u= (x^2)+(y^2) …