A rate of change function is given by $\frac{dx}{dt}=\sqrt{t}+t^5$dxdt=√t+t5 :

Determine $x\left(t\right)$x(t). Use $C$C as the constant of integration.

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Approx 3 minutes

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A rate of change function is given by $\frac{dy}{dx}=\left(4x+\frac{1}{x}\right)\left(5x-\frac{2}{x}\right)$dydx=(4x+1x)(5x−2x):

Determine $y\left(x\right)$y(x) given that $\frac{dy}{dx}=9-\frac{1}{\sqrt{x}}$dydx=9−1√x and $y=4$y=4 when $x=16$x=16.

Use $C$C as the constant of integration.

Outcomes

M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods