Compute the derivatives of the following functions.

Question

Compute the derivatives of the following functions. You may use any derivative rules.

(a) f(x) = x² − 2x.

(b) g(x) = 3x(x³ − 1).

(c) h(t) = (3t² − 9 / 2t³ + 5t) + 3/t

Answer 1

a) f'(x) = 2x-2

b) g'(x) = 12x^3 - 3

c) h'(t) =((2t^3 +5t)(6t) - (3t^2-9)(6t^2+5))/(2t^3+5t)^2 -3/t^2 mostly the quotient rule, then expand, simplify

= (12t^4 -30t^2 - 18t^4 -15t^2 +54t^2 +45)/(4t^6 +20t^4 +25t^2) - 3/t^2

= (-6t^4 +9t^2 +45)/(4t^6+20t^4 +25t^2) - 3/t^2

unless you meant

h(x)=3t^2 -9/t^3 +5t +3/t

then

h'(t)= 6t +27/t^4 +5 -3/t^2