Question

How do you find the derivative of `r(x)= (0.3x^2-4.2x+9.2)^1.5`?

Answer 1

`r'(x)= (0.9x-6.3)sqrt(0.3x^2-4.2x+9.2)`

Explanation:

`r(x)= (0.3x^2-4.2x+9.2)^1.5`

`r(x)= (0.3x^2-4.2x+9.2)^(3/2)`

`r'(x)= 3/2(0.3x^2-4.2x+9.2)^(1/2) * (0.3x^2-4.2x+9.2)'`

`r'(x)= 3/2(0.3x^2-4.2x+9.2)^(1/2) * (0.6x-4.2)`

`r'(x)= (0.9x-6.3)sqrt(0.3x^2-4.2x+9.2)`