NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Related rates (dy/dx=dy/dt x dt/dx)

Let $y=\left(x+5\right)^5$`y`=(`x`+5)5 be defined as a composition of the functions $y=u^5$`y`=`u`5 and $u=x+5$`u`=`x`+5.

a

Determine $\frac{dy}{du}$`d``y``d``u`.

b

Determine $\frac{du}{dx}$`d``u``d``x`.

c

Hence determine $\frac{dy}{dx}$`d``y``d``x`.

Easy

Approx 3 minutes

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

Apply differentiation methods in solving problems