Limits and Derivatives

Find the derivative of $f(x) = \sin x$ with respect to $x$ using first principles.

Find the derivative of $f(x) = \cos x$.

Find the derivative of $f(x) = 3x^2 + 5x - 7$.

Find the derivative of $f(x) = \log x$ with respect to $x$.

What is the derivative of $\frac{u}{v}$ with respect to $x$ (Quotient Rule)?