Unit 1-3 Memorization

Product Rule

d/dx [u·v] = u'v + uv'

Quotient Rule

d/dx [u/v] = (u'v − uv') / v²

Chain Rule

d/dx [f(g(x))] = f'(g(x)) · g'(x)

Derivative of sin x cos x

d/dx (sin x)cos x

Derivative of eˣ

d/dx (eˣ)eˣ

d/dx (sin x)

(cos x)

d/dx (cos x)

(−sin x)

d/dx (tan x)

(sec²x)

d/dx (cot x)

(−csc²x)

d/dx (sec x)

(sec x · tan x)

d/dx (csc x)

(−csc x · cot x)

d/dx (sin⁻¹x)

(1 / √(1 − x²))

d/dx (cos⁻¹x)

(−1 / √(1 − x²))

d/dx (tan⁻¹x)

(1 / (1 + x²))

d/dx (cot⁻¹x)

(−1 / (1 + x²))

d/dx (sec⁻¹x)

(1 / (|x|√(x² − 1)))

d/dx (csc⁻¹x)

(−1 / (|x|√(x² − 1)))

d/dx (eˣ)

(eˣ)

d/dx (aˣ)

(aˣ · ln(a))

d/dx (ln x)

(1 / x)

d/dx (logₐ x)

(1 / (x · ln(a)))