Formule di derivazione e integrazione elementari

y = f(x) + g(x) → y' = f'(x) + g'(x)

y = f(x) · g(x) → y' = f'(x) · g(x) + f(x) · g'(x)

y = ^f(x)/_g(x) → y' = ^{f'(x) · g(x) − f(x) · g'(x)}/_[g(x)]²

y = ¹/_f(x) → y' = −^f'(x)/_[f(x)]²

y = f[g(x)] → y' = f'[g(x)] · g'(x)

y = [f(x)]^g(x) → y' = [f(x)]^g(x) { g'(x) ln f(x) + g(x) ^f'(x)/_f(x) }

y = f(x) + g(x) → y' = f'(x) + g'(x)

y = f(x) · g(x) → y' = f'(x) · g(x) + f(x) · g'(x)

y = ^f(x)⁄_g(x) → y' = ^{f'(x) · g(x) - f(x) · g'(x)}⁄_[g(x)]²

y = ¹⁄_f(x) → y' = - ^f'(x)⁄_[f(x)]²

y = f[g(x)] → y' = f'[g(x)] · g'(x)

y = [f(x)]^g(x) → y' = [f(x)]^g(x) { g'(x) ln f(x) + g(x) ^f'(x)⁄_f(x) }

y = xⁿ → y' = nx^n-1

y = [f(x)]ⁿ → y' = n[f(x)]^n-1 · f'(x)

y = senx → y' = cos x

y = senf(x) → y' = f'(x) cos f(x)

y = cos x → y' = -senx

y = cos f(x) → y' = -f'(x) sen f(x)

y = ln x → y' = ¹⁄_x

y = ln f(x) → y' = ^f'(x)⁄_f(x)

y = log_a x → y' = ¹⁄_x log_a e

y = log_a f(x) → y' = ^f'(x)⁄_f(x) log_a e

y = e^x → y' = e^x

y = e^f(x) → y' = f'(x) e^f(x)

y = a^x → y' = a^x ln a

y = a^f(x) → y' = f'(x) a^f(x) ln a

y = tg x → y' = ¹⁄_{cos² x}

y = tg f(x) → y' = ^f'(x)⁄_{cos² f(x)}

y = ctg x → y' = - ¹⁄_{sen² x}

y = ctg f(x) → y' = - ^f'(x)⁄_{sen² f(x)}

y = arcsen x → y' = ¹⁄√_1-x²

y = arcsen f(x) → y' = ^f'(x)⁄√_1-[f(x)]²

y = arccos x → y' = - ¹⁄√_1-x²

y = arccos f(x) → y' = - ^f'(x)⁄√_1-[f(x)]²