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Please find the derivative of these exponential functions?

0 votes
PLEASE SHOW ALL WORK INVOLVED

1)y=(e^x * e^2)^3

2)y = 10e^(7x)

3) y = e^(sqrt(x))
asked Apr 15, 2013 in CALCULUS by andrew Scholar

5 Answers

0 votes

y = (ex × e2)^3

Apply the power rule ax ay = ax+y

y = [ex+2)]3

Apply the power rule (a(x+y))3 =a3x+3y

y = e3x+6

Apply derivative to each side

dy / dx = d / dx(e3x+6)

Recall : d / dx(eax+b) = aeax+b

dy / dx = 3e3x+6 .

answered Apr 15, 2013 by diane Scholar
0 votes

y = (ex × e2)^3

Apply the power rule ax ay = ax+y

y = [ex+2)]3

Apply the power rule (a(x+y))3 =a3x+3y

y = e3x+6

Apply derivative to each side

dy / dx = d / dx(e3x+6)2

Recall : d / dx(eax+b) = aeax+b

dy / dx = 3e3x+6 .

answered Apr 15, 2013 by diane Scholar
0 votes

y =(ex × e2)3

Apply the power rule ax ay = ax+y

y = [ex+2)]3

Apply the power rule (a(x+y))3 =a3x+3y

y = e3x+6

Apply derivative to each side

dy / dx = d / dx(e3x+6)2

Recall : d / dx(eax+b) = aeax+b

dy / dx = 3e3x+6 .

answered Apr 15, 2013 by diane Scholar
0 votes

y = 10e7x

Apply derivative to each side

dy / dx =d / dx(10e7x)

dy / dx = 10 [d / dx(e7x)]

Recall : Derivative exponential formulas d / dx(eax) = aeax

Therefore dy / dx = 10(7)e7x

dy / dx = 70(e7x).

 

answered Apr 15, 2013 by diane Scholar
0 votes

y = e√x

Put √x = t

y = et

Apply derivative to each side

dy = et dt

Substitute t = √x  and dt = [1 / 2√x)]dx in the  above diferential equation dy = et dt

Therefore dy = e√x [1 / 2√x)] dx

dy / dx = e√x [1 / (2√x)]

dy / dx = e√x/ 2√x .

 

answered Apr 15, 2013 by diane Scholar

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