What does d/dx (e^(3lnx))=?

Question

Thanks!!!!!!!!!!!!

Answer 1

We can reduce it prior to taking the derivative.

f(x) = e^(3 ln(x) )

f(x) = (e^ln(x) )^3

f(x) = x^3

Therefore,

f'(x) = 3x^2

Answer 2

Without simply blurting out an answer, notice first that the expression in question is defined only for x>0. Then simplify the expression. 3 ln(x) is the same as ln(x^3), and therefore the expression simplifies to x^3, again valid only for x>0. Differentiation using the exponent rule yields the result.

Answer 3

e^(3lnX) = e^lnx^3 = x^3, do d/dx (x^3) = 3x^2

Answer 4

d/dx e^u = e^u(du)
d/dx lnx = 1/x

d/dx (e^(3lnx))
u = 3lnx
du = 3/x
d/dx (e^u) = e^u du
d/dx (e^(3lnx)) = (e^(3lnx))(3/x) = (3e^(3lnx))/x

Answer 5

spectacular. Vincent's reaction that Darwin lined a financial ruin stated as: "problems with the thought" as whether it rather is a undesirable situation!!! it is so unhappy. Vincent is so thoroughly blind to what solid technology is. Vincent additionally seems to be unacquainted with honesty, to himself and to others. Vincent - scientists are meant to look in any respect the techniques their theories could desire to be incorrect. they're meant to brazenly, rather and vigorously challenge their own assertions. If the thought can put off decrease than such scrutiny and thinking, then it is an outstanding concept. i understand such thinking is thoroughly alien to the religious truthful who basically have self belief purely what their father and mom/clergy/bibles tell them, devoid of quesiton, devoid of doubt, devoid of any examination. Repeating a lie is basically as as undesirable as mendacity, extraordinarily while it is so truthfully on your capability to make certain that what you're announcing is in certainty a lie. basically examine THE e book your self!! Edward does the comparable situation. technology WORKS by ASKING QUESTIONS! it rather works by elevating doubts, by no longer uncomplicated ideals. Why is that this so no longer uncomplicated to comprehend? it rather is the comparable technique that placed adult men on the Moon and probes around Saturn. it rather is the comparable technique that developed vegetation so as that a huge share of 6 billion human beings can consume daily. it rather is the comparable technology that made it available which you would be able to head by way of existence devoid of assembly a smallpox or polio sufferer. Do you already know?? Scientists attempt to have open debate, to objective their theories, to ask the needed questions, and there are human beings like those that run creationist web content basically waiting to pounce on any little quote to declare the scientists are incorrect. And there are maximum of human beings like Edward and Vincent waiting for a raffle to blindly, unquestioningly repeat the costs devoid of thought what they're speaking approximately. They represent an uneducated military marching in the rationalization for lack of awareness.

Answer 6

E 3 Ln X

Answer 7

y =( e ^ (3lnx))
put , u = 3lnx , u ' = 3 / x , and ( e ^u) ' =( e ^ u )( u) '
y ' = [ e ^(3lnx)] (3 / x)
y ' = ( 3 / x) [ e ^(3lnx)]

Answer 8

e^(3lnx) = [e^(lnx)]^3

we know e^(lnx) = x, simplify:
x^3

so derivative of x^3 = 3x^2

Answer 9

The answer is 3x².
e^(3ln x) = e^(ln x³) = x³, because e^x and ln x are inverse
functions.
d/dx x³ = 3x².

Answer 10

(e^(3lnx)) = 3
d/dx (e^(3lnx)) = d/dx (3) = 0

You really should do your homework, though. =]