Formulas. Examples. (c)' = 0, (ax)' = a, (x^n)' = nx^{n-1}, (a/x)' = -(a/x^2), (square root of x)' = 1 / 2(square root of x), (e^x)' = e^x, (a^x)' = a^x * ln a, (ln x)' = 1/x, (log_a x)' = 1 / (x * lna). The derivatives of trigonometric functions. (sin x)' = cos x, (cos x)' = -sin x, (tan x)' = 1 / cos^x = 1 + tan^2 x, (cot x)' = -1 / sin^2 x = -(1 + cot^2 x), (arcsin x)' = 1 / square root (1 - x^2), (arccos x)' = -1 / square root (1 - x^2), (arctan x)' = 1 / (1 + x^2), (arccot x)' = -1 / (1 + x^2). Operations on the derivatives. Formulas. Examples. (f + g)' = f' + g', (f - g)' = f' - g', (c * f)' = c * f', (f * g)' = f' * g + f * g', (f / g)' = f'g - fg' / g^2. Derivatives of composite functions. [f(y)]' = f' * g'.