SOLUTION: Please find derivative and simplify: y= x^3ln3x y= e^ln5x y= e^lnx y= ln(5x+2)^3/ln(5x+2) i've completed over half of my homework, but i'm stuck right here...p

Question 59407: Please find derivative and simplify:
y= x^3ln3x
y= e^ln5x
y= e^lnx
y= ln(5x+2)^3/ln(5x+2)

i've completed over half of my homework, but i'm stuck right here...please help
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
(i) y = x^3 ln3x
This is a product and we apply product rule.
dy/dx = x^3 (1/3x)(3) + ln3x * 3x^2 [Derivative of lnx = 1/x]
= x^2 + 3x^2 ln3x [on simplifying]
= x^2(1 + 3ln3x)
(ii) y = e^ln5x
= 5x [because e^lnx = x only]
dy/dx = 5

(iii) y = e^lnx
= x
dy/dx = 1
(iv) I believe the question is y = [ln(5x+2)^3]/ln(5x+2)
= 3ln(5x+2)/ln(5x+2) [property of ln]
= 3
So dy/dx = 0
Good Luck!!!
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