Y = (1-x) (1-x ^ 2) ^ 2 (1-x ^ 3) ^ 3 derivative (logarithm) thank you

Y = (1-x) (1-x ^ 2) ^ 2 (1-x ^ 3) ^ 3 derivative (logarithm) thank you

LNY = ln (1-x) + 2ln (1-x ^ 2) + 3ln (1-x ^ 3) take logarithm on both sides to get y ′ / y = - 1 / (1-x) + 2 / (1-x ^ 2) * (- 2x) + 3 / (1-x ^ 3) * (- 3x ^ 2) = - 1 / (1-x) - 4x / (1-x ^ 2) - 9x ^ 2 / (1-x ^ 3) y ′ = - [1 / (1-x) + 4x / (1-x ^ 2) + 9x ^ 2 / (1-x ^ 3)] y = - [(1-x ^ 2) ^ 2 (1-x ^ 3)

Y = 2xsin (2x + 5), find the derivative of the function

From the derivative formula of y = f * g (F, G are two functions), we can see that:
y=f'*g+f*g'
And f (g) '= f' * g '
So y '= (2x)' * sin (2x + 5) + 2x * [sin (2x + 5)] '
=2sin(2x+5)+2xcos(2x+5)*2
=2sin(2x+5)+4xcos(2x+5)