Differentiation and Integration Formulas

These flashcards cover key differentiation and integration formulas essential for calculus exams.

What is the derivative of x with respect to x?

1

What is the derivative of ax with respect to x?

a

What is the derivative of x^n (where n ≠ 0)?

ax^(n-1)

What is the derivative of cos x?

-sin x

What is the integral of 1 with respect to x?

x + C

What is the integral of a with respect to x?

ax + C

What is the integral of x^n when n = -1?

ln |x| + C

What is the integral of sin x?

-cos x + C

What is the integral of cos x?

sin x + C

What is the integral of sec² x?

tan x + C

What is the derivative of sin x?

cos x

What is the derivative of tan x?

sec² x

What is the derivative of cot x?

-csc² x

What is the integral of csc² x?

-cot x + C

What is the derivative of sec x?

sec x tan x

What is the integral of sec x tan x?

sec x + C

What is the derivative of cosec x?

-csc x cot x

What is the integral of csc x cot x?

-csc x + C

What is the derivative of ln x?

1/x

What is the integral of e^x?

e^x + C

What is the derivative of a^x?

(ln a) a^x

What is the integral of sin x?

-cos x + C

What is the integral of tan x?

-ln |cos x| + C

What is the derivative of sec x?

sec x tan x

What is the integral of sec x?

ln |sec x + tan x| + C