1. The problem is to find the derivative of the function $f(x) = x^3 - 5x^2 + 6x - 2$.\n\n2. The formula for the derivative of a power function $x^n$ is $\frac{d}{dx} x^n = nx^{n-1}$.\n\n3. Apply the derivative to each term separately:\n$$\frac{d}{dx} (x^3) = 3x^2$$\n$$\frac{d}{dx} (-5x^2) = -5 \cdot 2x = -10x$$\n$$\frac{d}{dx} (6x) = 6$$\n$$\frac{d}{dx} (-2) = 0$$\n\n4. Combine the results:\n$$f'(x) = 3x^2 - 10x + 6$$\n\n5. This is the derivative of the polynomial function.\n\n6. Next, find the derivative of the trigonometric function $g(x) = \sin x + \cos x$.\n\n7. The derivatives of sine and cosine are:\n$$\frac{d}{dx} \sin x = \cos x$$\n$$\frac{d}{dx} \cos x = -\sin x$$\n\n8. Apply these to $g(x)$:\n$$g'(x) = \cos x - \sin x$$\n\n9. Finally, find the derivative of the exponential and logarithmic function $h(x) = e^x + \ln x$.\n\n10. The derivatives are:\n$$\frac{d}{dx} e^x = e^x$$\n$$\frac{d}{dx} \ln x = \frac{1}{x}$$\n\n11. So,\n$$h'(x) = e^x + \frac{1}{x}$$\n\nThese exercises cover polynomial, trigonometric, exponential, and logarithmic derivatives, which are fundamental in first-year calculus.