



 
Bader, I think you want to find dy/dx. This is an exercise in using the chain rule. Let's try a slightly different problem. Find dy/dx if y = tan(x^{2} + 1) This function is composed of two functions, the function f(s) = tan(s) and g(s) = s^{2} + 1. I have used the variable s here rather than x because the variable is only used to help describe how the function operates. f is the tangent function and g is the function "square the variable and add 1". The function y is constructed from f and g by
that is
The chain rule says that
The derivative of the tangent function is the square of the secant function so
But g(x) = x^{2} + 1 and g'(x) = 2x so
Now try f(x) = sin(2x) Penny  


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