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

##### 1 Answer

Dec 21, 2016

# (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

By treating

# \ \ \ \ \ (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

# \ \ \ \ \ (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 #