Question

How do you find the derivative of `18lnx+x^2+5`?

Answer 1

`18/x+2x`

Explanation:

Through the sum rule, to find this function's derivative, add each part's derivative to one another:

Thus, we just need to find the derivative of each part:

`d/dx(18lnx)=18d/dx(lnx)=18(1/x)=18/x`

Recall that `d/dx(lnx)=1/x`, and that `18` is just a constant being multiplied, which we can multiply by the derivative of `lnx`.

Through the power rule, we see that

`d/dx(x^2)=2x`

And, since `5` is a constant,

`d/dx(5)=0`

Thus, the function's derivative is

`18/x+2x+0" "=" "color(blue)(18/x+2x`