1 votes 1 votes What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$ Calculus nielit2016mar-scientistb engineering-mathematics calculus integration definite-integral + – admin asked Mar 31, 2020 • retagged Oct 23, 2020 by Krithiga2101 admin 542 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Integrating the function first and then applying limits, we get: $\Phi (x)=\frac{2}{3}\left [ (x^{2})^{1.5}-0 \right ]$ $=$ $\frac{2}{3}x^{3}$ $\frac{d}{dx}(\frac{2}{3}x^{3})=2x^{2}$ Option A is correct. haralk10 answered Mar 31, 2020 haralk10 comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Apply Newton Leibniz rule s_dr_13 answered Mar 22, 2022 s_dr_13 comment Share Follow See all 0 reply Please log in or register to add a comment.