Calculus/calculus 1

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Expert: - 3/28/2008


Question
PLEASE REPLY BY TONIGHT!! REALLY APPRECIATE IT!! and also if u can explain the answers in steps..=D

1)Use the derivatives of the hyperbolic function sinhx + coshx to drive the derivation of cothx

2) show that the function f(x)= x+1 for x<2
                         f(x)= 2x-1 for x>2
is not differentible at x=2

3) find y' for y^2=x^2-6x+4cos(y)

4) find the derivative of f(x) = x^2sinx^2 - x^3e^cosx

Answer
I didn't turn it on until this morning, but here goes.

1) Since coth(x) = sinh(x)/cosh(x), the quotient rule can be used.  Remember that sinh(x) is (e^x - e^-x)/2 and cosh(x) is (e^x + e^-x)/2.

2) Take the derivative from the positve side and the negative side and show that they are not equal.

3)  Note that y' can be found by the chain rule and resubstitution of y back into the equation to get it terms of x.

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