Help with logarithmic differentiation?

Question

(a) y = (x)^(x)^(x^4)

(b) y = (√x)^(√x) e^(x^2)

(c) y = π + 2^x + x^2 + x^(1/x)

(d) ∫ ([ln (5x - 10) ]^7) / (3x - 6) dx

(e) ∫ 1 / (3x - 27) (2x - 10) dx

Answer 1

It's so hard to be written.

I'll give you number one as an example.

y = x^x^x^4

ln y = x^x^4 . ln x

y1 = x^x^4

ln y1 = x^4 . ln x

y'1/y1 = (4x^3 . ln x) + (x^4 . 1/x)

y'1 = x^x^4 . (4x^3 . ln x + x^3)

ln y = x^x^4 . ln x

y'/y = (y'1 . ln x) + (x^x^4 . 1/x)

y' = y((y'1 . ln x) + (x^x^4 . 1/x))

Subtitute back y and y'1 and you get te answer.