Question

Pls explain answer c and d?

Answer 1

`\bf a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------\\\\ c)\\\\ f(x)=\cfrac{1}{√(x)}\implies f(x)=x^{-(1)/(2)}\implies \cfrac{dy}{dx}=-\cfrac{1}{2}x^{-(1)/(2)-1}\implies \cfrac{dy}{dx}=-\cfrac{1}{2}x^{-(3)/(2)}`


`\bf \cfrac{dy}{dx}=-\cfrac{1}{2}\cdot \cfrac{1}{x^{(3)/(2)}}\implies \cfrac{dy}{dx}=-\cfrac{1}{2}\cdot\cfrac{1}{\sqrt[2]{x^3}}\implies \cfrac{dy}{dx}=-\cfrac{1}{2√(x^3)}\\\\ -------------------------------\\\\ d)\\\\ f(t)=t^3+3t^2-6\implies \cfrac{dy}{dt}=3t^2+6t^1-0\implies \cfrac{dy}{dt}=3t^2+6t`