Calculus Differentiation Formulas

Flashcards covering common differentiation formulas for various functions and fundamental calculus rules such as the product rule and quotient rule, based on the provided lecture notes.

d/dx (c), where c is a constant

0

d/dx (x^n)

nx^(n-1)

d/dx (sin x)

cos x

d/dx (cos x)

-sin x

d/dx (tan x)

sec^2 x

d/dx (csc x)

-csc x cot x

d/dx (sec x)

sec x tan x

d/dx (cot x)

-csc^2 x

d/dx (e^x)

e^x

d/dx (a^x)

a^x ln a

d/dx (log_b x)

1 / (x ln b)

d/dx (ln x)

1 / x

d/dx (sin⁻¹ x)

1 / sqrt(1 - x^2)

d/dx (cos⁻¹ x)

-1 / sqrt(1 - x^2)

d/dx (tan⁻¹ x)

1 / (1 + x^2)

d/dx (csc⁻¹ x)

-1 / (|x| sqrt(x^2 - 1))

d/dx (sec⁻¹ x)

1 / (|x| sqrt(x^2 - 1))

d/dx (cot⁻¹ x)

-1 / (1 + x^2)

Product Rule: d/dx (f(x)g(x))

f'(x)g(x) + f(x)g'(x)

Quotient Rule: d/dx (f(x)/g(x))

(g(x)f'(x) - f(x)g'(x)) / (g(x))^2