Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

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

Answer 2

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