Question

Differentiate y=(x^2-5x)inx?

Answer 1

Presuming that in x was meant to be `ln x`, the answer is `(2x-5)lnx + x-5`

Explanation:

We will be using the product rule here. The product rule states that for `f(x) = g(x)h(x)`, that is to say, the product of functions `g(x)` and `h(x)`, `(df)/dx = (dg)/dx h(x) + g(x)(dh)/dx`.

With `g(x) = x^2-5x` and `h(x) = ln x`, we know that `(dg)/dx = 2x - 5, (dh)/dx = 1/x`

Thus:

`(df)/dx = (2x-5)ln x + (x^2-5x)/x`

Which, for any `x!=0` is...

`(df)/dx = (2x-5)lnx + x-5`