find derivative

Question

#14.  y=ln(6x+7)^1/5

 

#26. y=6ln(x^4-2)

 

#30. 7e^4√x+8

 

#32.f(x)= 8+9x ln x

 

#34.y=ln √x^2-5

Answer 1

Jenny,

 

#14. y=ln(6x+7)^(1/5) .   Then dy/dx = (1/5)(6x + 7)^(-4/5)(6) / (6x+7)^(1/5) = 6 /[5 (6x+7)(5/5)] = 6/[5(6x+7)].

#26. y=6ln(x⁴-2) .  Then dy/dx = 6 (4x³)/(x⁴ - 2) =  24x³ / (x⁴ - 2).

#30. 7e^[4√(x+8)] .    Then dy/dx = 7[2(x+8)^(-1/2)] e^[4√(x+8)] = 14 e^[4√(x+8)] / (x+8)^(1/2).

#32.f(x)= 8+9x ln x.  Then df(x)/dx = 0 + 9  ln x + 9x(1/x) = 9 [ 1 + ln x].

#34.y=ln √(x²-5) . Then dy/dx = {1/[(x² - 5)^(1/2)]} [(1/2)2x] = x/[(x² - 5)^(1/2)].