Question

How do you differentiate `x^2 + 8x + 3 / sqrtx` using the quotient rule?

Answer 1

`2x+8-3/(2x^(3/2))`

Explanation:

The quotient rule is not required here as we have a sum of terms which can be differentiated using the `color(blue)" power rule"`

`d/dx(ax^n)=nax^(n-1)`

Before applying this rule we need to rewrite the term`3/sqrtx`
`rArr3/sqrtx=3/x^(1/2)=3x^(-1/2)`

We now have: `x^2+8x+3x^(-1/2)`

`rArrd/dx(x^2+8x+3x^(-1/2))=2x+8-3/2x^(-3/2)`

`=2x+8-3/(2x^(3/2))`