Partial Derivative dz/dx of cosh(2x - y), etc.

[Guest]

Two Questions:

When taking the partial derivative of cosh(2x-y) is dz/dx = 2sinh(2x)

And how would you partially differentiate

f(x,y) = Integral from x to y of t^2-1 dt

dz/dx = ?
dz/dy = ?

 

[pka]

\(\displaystyle \L
z(x,y) = \int\limits_x^y {\left( {t^2 - 1} \right)dt} \quad \Rightarrow \quad \left\{ \begin{array}{l}
\frac{{\partial z}}{{\partial y}} = \left( {y^2 - 1} \right) \\
\frac{{\partial z}}{{\partial x}} = - \left( {x^2 - 1} \right) \\
\end{array} \right.\)