Is My Logarithmic Differentiation of This Complex Function Correct?

[superjen]

y = (sin2x)³(x⁴-4x)⁶ divided by (cosx) + e^3x

i came out with an answer

y' = (sin2x)³(x⁴-4x)⁶divided by (cosx) + e^3x [3cot2x + 24x³-24 divided by x⁴-4x + Tanx + 3x


could someone tell me if I am right?
i don't know if this is what I am supose to do,
if you want me to write out exactly what i did i can.

 

[HallsofIvy]

You titled this "logarithmic differentiation" but I see no logarithm.

 

[superjen]

i'm supose to solve it using logartimic differentiation, so when i do it out i get

lny = 3ln(sin2x) + 6ln(x^4-4x) - ln(cosx) + 3xln(e)

 

[Mark44]

i'm supose to solve it using logartimic differentiation, so when i do it out i get

lny = 3ln(sin2x) + 6ln(x^4-4x) - ln(cosx) + 3xln(e)

Your last two terms came from cos(x) + e^(3x) in the denominator. ln(a + b) $\neq$ ln a + ln b