Question

What are the derivatives? Thanks

a) y = log(base2)(4-9x)

b) y = x^(8x)

Answer 1

in general for y = log_a u
dy/dx = (1/ln a)(1/u)du/dx

so for the above
dy/dx = (1/ln2)(-9)/(4-9x)

for the second one take ln of both sides
y = x^(8x)
ln y = ln (x^(8x))
ln y = (8x)(ln x)
now take the derivative implicityly using the product rule on the right side

y'/y = 8x(1/x) + 8(ln x)
y' = y[8 + 8ln x)
= (8+8ln x)(x^(8x))