Verify that the solution of u"=f(x), u(0)=0, u(1)=0 given by u(x)= the integration from 0 to 1 of k(x,y)f(y)dy. Use Leibniz rule.
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This shows how to use the Leibniz rule to verify a solution.
Exponential Derivatives of Composite Functions : Chain Rule and Leibnitz Notation
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The Chain Rule states how to differentiate composite functions
If and be differentiable, then the derivative of the composite function is
In Leibnitz notation, if and , then .
The derivative of the exponential function is
6. Find .