Question

Help with derivative?

Answer 1

a) The function f(x) = 0.01x³

Apply derivative on each side with respect of x.

Apply the formula d/dx(xⁿ)= n x^n-1

f'(x) = 0.01(3)x^3-1

^{f'(x) = 0.03x2}

^{f'(2) = 0.03(2)2}

= 0.03(4)

f'(2) = 0.12.

Answer 2

b) The function g(x) = 0.12x^1/2

Apply derivative on each side with respect of x.

g'(x) = 0.12(1/2)x^(1/2)-1

g'(x) = 0.06x^-1/2

g'(3) = 0.06(3)^-1/2

 = 0.06/(3)^1/2

 = 0.06/√3

 = 0.06/1.732

= 0.0346

g'(3) = 0.03.

Answer 3

c) The function h(x) = 0.06x

Apply derivative on each side with respect of x.

Apply the formula d/dx(x) = 1

h'(x) = 0.06

h(4) = 0.06.

Answer 4

d) The function j(x) = 1.3x^-1

Apply the formula d/dx(xⁿ)= n x^n-1

j'(x) = 1.3 (-1)x^-1-1

= - 1.3x^-2

= - 1.3/x²

j'(5) = - 1.3/(5)²

= - 1.3/25

= - 0.052

j'(5) = - 0.05.