Question

How do you find the derivative of `g(x)=sqrt(5-3x)`?

Answer 1

Let h(x) = x^(1/2)# and #k(x) = 5-3x#

so `g(x) = sqrt(5-3x) = h(k(x))`

`(d g(x))/(dx) = (d h(k(x)))/(d k(x))*(d k(x))/(dx)`

`=(1/2)(k(x))^(-1/2)*(-3)`

`= (-3/2)*1 /sqrt(5-3x)`

`= - 3/(2sqrt(5-3x))`