h(t) = [sqrt(t) ]*[(1-tē)]
find derivative using product rule any help on how to solve this would be nice i cant come to the awnser in the back of my book :/
also how do u do squareroot and other signs i see most people use when posting on forums?
h(t) = [sqrt(t) ]*[(1-tē)]
find derivative using product rule any help on how to solve this would be nice i cant come to the awnser in the back of my book :/
also how do u do squareroot and other signs i see most people use when posting on forums?
Just in case a picture helps...
... where
... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to t
Spoiler:
__________________________________________
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
$\displaystyle h(t)=\sqrt{t}(1-t^2)$
Taking $\displaystyle f(t)=\sqrt{t}$ and $\displaystyle g(t) = (1-t^2) $
$\displaystyle f'(t) = \frac{1}{2\sqrt{t}} $ and $\displaystyle g'(t) = -2t $
$\displaystyle h'(t) = f(t)g'(t) + g(t)f'(t) $
$\displaystyle h'(t) = -2t\sqrt(t) + \frac{(1-t^2)}{2\sqrt{t}} $
If simplified,
$\displaystyle h'(t) = \frac{(1-t^2)}{2\sqrt{t}} - 2t^{\frac{3}{2}}$