Differentiation

Archimedes wrote: »

a) x/7

Well, [latex]\displaystyle\frac{x}{7}[/latex] is the same thing as [latex]\displaystyle\frac{1}{7}\mbox{x}[/latex]. So, differentiate [latex]\displaystyle\mbox{x}[/latex] and, at the very end, multiply it by [latex]\displaystyle\frac{1}{7}[/latex]. So, what's the derivative of x with respect to x?

b) 1/4 √x

For this one, change the [latex]\displaystyle\sqrt{x}[/latex] into its indice form, i.e. [latex]x^{\frac{1}{2}}[/latex]. Now, differentiate [latex]x^{\frac{1}{2}}[/latex] and, again at the very end, multiply it by [latex]\displaystyle\frac{1}{4}[/latex].

When there's a constant (a number) in front of the variable (in both of these cases, x), you can, basically, ignore it until the end and then multiply it by the derivative of the x.