Consider the curve defined by r(t) = (cos(t) + t sin(t))+ (sin(t)- t cos(t))] for t > 0. (a) Compute the derivative (t) of the curve above. Simplify your answer. (b) Use the result above to compute |u(t). The Pythagorean identity cos² (t) + sin² (t) = 1 will be helpful here. Also, we are assuming t> 0 for convenience. (c) Use the result above to find the arc length of F(t) for ≤t≤ π.

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Q: 1. Prove that the derivative of tan(x) is sec²(x) directly from the definition of the derivative.…

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Q: 1. Prove that the derivative of tan(x) is sec² (x) directly from the definition of the derivative.…

A: The derivative of fx with respect to x is defined as:limh→0fx+h−fxh