Differentiate y = x^2 - 2x-3 + e^3x + 2ln(x)

The above function has several components with different rules on how to differentiate each of them. For each:(1) y = x²dy/dx = 2x This follows the general rule of differentiating polynomials: y = xⁿ, dy/dx = nx^n-1(2) y = -2x^-3dy/dx = (-2)(-3)x^-4 = 6x^-4This follows the same rule as above except there is also an integer and a sign change which needs to be taken into account(3) y = e^3xdy/dx = 3e^3xThis follows the rule for differentiating exponential functions: y = e^nx, dy/dx = ne^nx. (4) y = ln(x)dy/dx = 2/xThis follows the rule for differentiating natural logarithms: y = ln(x), dy/dx = 1/x(5) The total differential is therefore:dy/dx = 2x + 6x^-4 +3e^3x +2/x