Question

Find the partial derivatives of `m = ln(qh-2h^ 2)+2e(q-h^2+3)^4-7`?

Answer 1

`(partial m)/(partial q) = 1/(q-2h) + 8e(q-h^2+3)^3`

`(partial m)/(partial h) = (q-4h)/(qh-2h^2) - 16eh(q-h^2+3)^3`

Explanation:

If

`m = ln(qh-2h^ 2)+2e(q-h^2+3)^4-7`,

then (assuming that `q` and `h` are variables) the partial derivatives are:

By treating `h` as constant we get:

`\ \ \ \ \ (partial m)/(partial q) = 1/(qh-2h^2)*h + 2e*4(q-h^2+3)^3*1`
`:. (partial m)/(partial q) = 1/(q-2h) + 8e(q-h^2+3)^3`

And by treating `q` as constant we get:

`\ \ \ \ \ (partial m)/(partial h) = 1/(qh-2h^2)*(q-4h) + 2e*4(q-h^2+3)^3*(-2h)`
`:. (partial m)/(partial h) = (q-4h)/(qh-2h^2) - 16eh(q-h^2+3)^3`