📢 Shares

The derivative of sin(2x² + 3x) is found using the chain rule, differentiating the outer sine function and the inner quadratic function separately, and then multiplying the results: cos(2x² + 3x) * (4x + 3).

The derivative of the function f(x) = 3x^2 - 4x + 7 is f'(x) = 6x - 4.

The problem involves finding the value of x in an expression where the greatest common factor (GCF) of two terms is given. The GCF is used to determine the value of x, but the problem cannot be solved without additional information about the variable y.

To find the area of the shaded region, subtract the area of a circle (formed by two semicircles) from the area of the enclosing rectangle.

The equation "\[\sqrt{(M-4)(M+4)} = 3\]" was solved by squaring both sides, expanding, simplifying, and taking the square root to find the solutions M = 5 and M = -5.

To find y when x = 4, substitute x = 4 into the equation y = 2x² - 3x + 1. Solving gives y = 21.

The limit of (1 + 1/x)^x as x approaches infinity is e.

The limit of sin(x)/x as x approaches 0 is 1, determined using L'Hôpital's rule.

The limit of (x² - 1) / (x - 1) as x approaches 1 is 2. This is found by factoring the numerator (difference of squares) and canceling the common factor of (x - 1).

The solution to the equation 25^x = 125 is x = 3/2. Squaring this value gives x^2 = 9/4.