create a function that uses newton's method to solve cos(sin(x))*log(log(x))-x^3+6 in matlab

To create a function that uses Newton's method to solve the equation cos(sin(x))*log(log(x))-x^3+6 in MATLAB, you can follow these steps:

1. Define the equation as a function. Let's call it equation. This function will take x as the input and return the value of the equation at that x:

main.m
function y = equation(x)
    y = cos(sin(x))*log(log(x))-x^3+6;
end
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2. Create a function to implement Newton's method. Let's call it newtonMethod. This function will take guess as the initial guess and tolerance as the desired level of accuracy. It will return the estimated root using Newton's method:

main.m
function root = newtonMethod(guess, tolerance)
    x = guess;
    while abs(equation(x)) > tolerance
        derivative = (equation(x + tolerance) - equation(x)) / tolerance;
        x = x - equation(x) / derivative;
    end
    root = x;
end
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3. Now, you can call the newtonMethod function with an initial guess and tolerance to solve the equation:

main.m
initialGuess = 1.5;
desiredTolerance = 0.00001;
estimatedRoot = newtonMethod(initialGuess, desiredTolerance);

fprintf("Estimated root: %f\n", estimatedRoot);
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This code defines a function equation to represent the equation you provided and then implements the Newton's method in the newtonMethod function. Finally, it calls newtonMethod with an initial guess and tolerance to estimate the root of the equation.

Note: Make sure to choose a suitable initial guess and tolerance value based on the specific characteristics of the equation and the precision required for your application.