Question

How do you differentiate `(x^2+3)sqrt(x+2)`?

Answer 1

`d/dx ( (x^2+3)sqrt(x+2)) =(5x^2 +8x +3)/(2sqrt(x+2))`

Explanation:

Using the product rule:

`d/dx ( (x^2+3)sqrt(x+2)) = (d/dx(x^2+3)) sqrt(x+2) + (x^2+3)(d/dx sqrt(x+2))`

`d/dx ( (x^2+3)sqrt(x+2)) =2x sqrt(x+2) + (x^2+3)/(2sqrt(x+2))`

Now simplifying:

`d/dx ( (x^2+3)sqrt(x+2)) =(4x (x+2) + (x^2+3))/(2sqrt(x+2))`

`d/dx ( (x^2+3)sqrt(x+2)) =(4x^2 +8x + x^2+3)/(2sqrt(x+2))`

`d/dx ( (x^2+3)sqrt(x+2)) =(5x^2 +8x +3)/(2sqrt(x+2))`