Question

Question #e8e24

Answer 1

`d/dxf(x)=(-3)/(2x^(3/2))+1/sqrtx`

Explanation:

`f(x)=(3+2x)/(sqrtx)`

This can also be written as `->`

`f(x)=3/sqrtx+(2x)/sqrtx`

`f(x)=3/sqrtx+(2*sqrtx*sqrtx)/sqrtx`

`f(x)=3/sqrtx+(2cancel(sqrtx)sqrtx)/cancel(sqrtx)`

`f(x)=3/sqrtx+2sqrtx`

Now you can differentiate both sides with respect to `x`

The power rule is `d/dxx^n=nx^(n-1)`

`d/dxf(x)=d/dx3/sqrtx+d/dx2sqrtx`

`d/dxf(x)=(-3)/(2x^(3/2))+1/sqrtx`