Question

Calculate the derivative of the function.
Using Chain Rule

r(x) = (0.1x^2 − 4.2x + 9.5)^1.5

Answer 1

((3/2)((0.1x^2-4.2x+9.5)^.5) * (.2x-4.2)

Answer 2

a substitution \[u=0.1x^{2}-4.2x+9.5\] would simplify the problem to
\[r(x)=u^{1.5}\]

Answer 3

by chain rule, \[r \prime(x)=\frac{ dr }{ du }\frac{ du }{ dx }\]

Answer 4

\[\frac{ dr }{ du }=1.5u^{0.5}\] and \[\frac{ du }{ dx }=0.2x-4.2\]

Answer 5

i understand that part now. what would be the next step?

Answer 6

multiply the two expressions obtained in (dr/du) and (du/dx)