Question

Can you please explain how to differentiate an equation? specifically, how to get from this:h(t) = -16t^2 + 72t + 24 to this:h'(t) = -32t + 72I am a parent trying to help my child. looks vaguely familiar but it's been a long time, if you know what I mean! Thank you!

Answer 1

`h(t)=-16t^2+72t+24`

To differentiate an equation as given you can use the next:

Derivates of powers:

`\begin{gathered} f(x)=x^n \\ f^(\prime)(x)=nx^(n-1) \\ \\ \\ f\mleft(x\mright)=x \\ f^(\prime)(x)=1 \\ \end{gathered}`

Derivate of a constant:

`\begin{gathered} f(x)=c \\ f^(\prime)(x)=0 \end{gathered}`

You have in the given equation two powers (the fist two terms) and a constant (las term (24)):

`\begin{gathered} h^(\prime)(t)=-2(16t)^(2-1)+72(1)+0 \\ \\ h^(\prime)(t)=-32t+72 \end{gathered}`