# Equation differentiation and substitution

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Ahmed Abed on 12 Jun 2019
Commented: Ahmed Abed on 13 Jun 2019
Sorry if the question has been asked before.
I have two equations, such as
lts=22*(ss/mor)^2.2/(w*(29+N^0.4)) .... equation 1
N=(22*(ss/mor)^(-2.2)/(w*lts)-29)^(5/2) ..... equation 2
where ss, mor, w, lts, and N are variables.
the solution is to diffrentiate the first equation with respect to N then subsititue the second equation in the resulting equation from the differentiation process. Please, could you suggest a solution? Thanks in advance.

Kaustav Bhattacharya on 13 Jun 2019
You can use 'syms' to symbolize N, w, ss and mor. Define the first equation 'Its'. Nest use the 'diff' function { diff(lts,N) } to partially differentiate.
Ahmed Abed on 13 Jun 2019
Hi Kaustav, thanks for the answer
{ diff(lts,N) }=-(44*(ss/mor)^(11/5))/(5*N^(3/5)*w*(N^(2/5) + 29)^2)
this part can be easly solved as you suggested. But how to subsititute equation 2
{N=(22*(ss/mor)^(-2.2)/(w*lts)-29)^(5/2)} in the resulting equation of the diffrentiation process and simplify the result?

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