I am new to Mathematica. i hope to have the software next week so please excuse the unusual syntax.
p(y) means p is a function of y.
u(p) means u is a function of p
p(x) is the value of p when y=x
I need to differentiate wrt y the following: p(x)integral between x and h((1/p(y) * u(p) * dp/dy * dy)
Differentiating by parts i get
u * dp/dy + dp/dyintegral between x and h((1/p) * u * dp/dy* dy)
Is this correct?
This is the same question you posted on mathematica.stackexchange, and with the same syntax issue:
Integral between x and h((1/p(y) * u(y) * dp/dy * dy)
Do you mean the integral of (1/p(y) * u(y) * dp/dy * dy from x to h?
If so, note that the value of the integral does not depend upon the dummy variable y, so its derivative with respect to y will be zero.
Apologies u is a function of p.i.e u(p).I have corrected (edited) the script in the original question
P is also a function of y ,p(y)=a+by where a and b are constants.
The derivative of the whole thing is still 0. For
p(y) = a + b y
we have
p'(y) = b
so the integrand
1/p(y) * u(p) * p'(y)
collapses to
\frac{b u(y)}{a + b y}.
Thus the entire expression whose derivative you want is:
p(x) \int_x^h \frac{b u(y)}{a + b y} dy.
The derivative of that with respect to y — which is what you asked for — is still 0.
Or did you really
want the derivative with respect to x??