Question

What is the derivative of f(x)= 1/5(x^2 + 2)^5/2?

Answer 1

`f(x)=\cfrac{1}{5}(x^2+2)^{(5)/(2)}\implies \cfrac{df}{dx}=\cfrac{1}{5}\stackrel{\textit{chain~rule}}{\left[\cfrac{5}{2}(x^2+2)^{(3)/(2)} \cdot (2x) \right]} \\\\\\ \cfrac{df}{dx}=(x^2+2)^{(3)/(2)}(x)\implies \cfrac{df}{dx}=x√((x^2+2)^3)`

Answer 2

x(x^2+2)^3/2

Explanation:

y'=1/2(x^2+2)^3/2.2x

= x(x^2+2)^3/2