Step-by-step explanation:
For implicit, you take the derivative of entire equation. When it is a function of 'y', you must multiply derivative by ' dy/dx'.
For this example, f(x) = x^4, g(y) = cot(y)
After differentiating, solve for 'dy/dx':
The probability of losing per flip is 1/2. Multiply 1/2 by itself 6 times since the condition is asking for the probability for the person to lose 6 times in a row. 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64. The answer is 1/64.