calculus
h(x)= integral from (1, 1/x) arctan(2t)dt
part 1: let U= 1/x and du= ?
-> using u=1/x, we can write h(x)= integral from (1, 1/x) arctan (2t)dt as h(u)= integral from (1,u) arctan(2t)dt and h'(u)= arctan (2)
Part 2: By the chain Rule, for functions h(u) and u(x), we have:
-> dh/dx= ______ du/dx
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Answers
By the Chain Rule, the derivative of a composite function with respect to its innermost variable is found by multiplying the derivatives of its outermost function with respect to the innermost variable, and its innermost variable with respect to its outermost variable. In this case, we can write dh/dx= dh/du*du/dx. Since h'(u)= arctan(2), we can write dh/dx= arctan(2)*du/dx.
