formula

x - f(x)/f'(x) right?

so

1 - 1.1x^1.4 - cosx / 1.54x^.4 + sinx .......... ? right?

then what??

The "formula" is

x2 = x1 -[f(x1) / f'(x1)]

x3 = x2 -[f(x2) / f'(x2)]

and so on....

where

x1, x2, x3 are read x sub 1, x sub 2, x sub 3, respectively.

x2 is nearer to the correct root than x1.

x3 is nearer to the correct root than x2.

and so on...

So your "formula" for your Problem should be

x2 = x1 -[(1.1(x1)^(1.4) -cos(x1)) / (1.54(x1)^(0.4) +sin(x1))]

{Too many parentheses and brackets? Yes. You need to practice that. }

Then just substitute the seed root, or starting solution, x1 = 1 in the formula to get x2.

x2 = 1 -[(1.1(1)^(1.4) -cos(1)) / (1.54(1)^(0.4) +sin(1))]

{In the cos(1) and sin(1), the 1 is 1 radian. So use your calculator's angle mode in radians.}

x2 = 1 -[(1.1(1) -0.540302306) / (1.54(1) +0.841470985)]

x2 = 1 -0.235021841

x2 = 0.764978159

Then, for the second iteration,

x3 = 0.764978159 -[(1.1(0.764978159)^(1.4) -cos(0.764978159)) / (1.54(0.764978159)^(0.4) +sin(0.764978159))]

Whoa, if you can navigate that, you are good.

Go up to x4 or x5 or x6, if you like.

{Normally, if x1 is close enough to the correct solution, you need up to x4 only.}