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!

Respuesta :

[tex]h(t)=-16t^2+72t+24[/tex]

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

Derivates of powers:

[tex]\begin{gathered} f(x)=x^n \\ f^{\prime}(x)=nx^{n-1} \\ \\ \\ f\mleft(x\mright)=x \\ f^{\prime}(x)=1 \\ \end{gathered}[/tex]

Derivate of a constant:

[tex]\begin{gathered} f(x)=c \\ f^{\prime}(x)=0 \end{gathered}[/tex]

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

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