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1 a) Differentiate each of...

1 a) Differentiate each of the following functions, identifying any general rules of calculus that you use, and simplify your answers as far as possible

F(x) = sec(5x)In(cos(5x)) (-1/10 pie < x < 1/10 pie)

F(x) = e^arcsinx / √1- x^2 (-1 < x < 1)

b) Consider the function f(x) = 2x In x – 1

Show that the question f(x) = 0 has a solution in the interval (1,2)

Show that, for this function f, the Newton-Raphson formula can be expressed as

Xn+1 = xn + ½ / 1 + In xn (n= 0,1,2....)

Please show all working out steps

Thank you for your help

F(x) = sec(5x)In(cos(5x)) (-1/10 pie < x < 1/10 pie)

F(x) = e^arcsinx / √1- x^2 (-1 < x < 1)

b) Consider the function f(x) = 2x In x – 1

Show that the question f(x) = 0 has a solution in the interval (1,2)

Show that, for this function f, the Newton-Raphson formula can be expressed as

Xn+1 = xn + ½ / 1 + In xn (n= 0,1,2....)

Please show all working out steps

Thank you for your help

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