Calculus Derivatives and Integrals

Flashcards covering basic derivative and integral rules.

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 with respect to x?

nx^(n-1)

What is the derivative of ln(x) with respect to x?

1/x

What is the derivative of e^x with respect to x?

e^x

What is the derivative of a^x with respect to x (for a>0, a≠1)?

(ln a) a^x

What is the derivative of sin^-1(x) with respect to x?

1/√(1-x^2)

What is the derivative of tan^-1(x) with respect to x?

1/(1+x^2)

What is the derivative of sec^-1(x) with respect to x?

1/(|x|√(x^2-1))

What is the integral of 1 dx?

x + C

What is the integral of a dx?

ax + C

What is the integral of x^n dx (where n ≠ -1)?

x^(n+1)/(n+1) + C

What is the integral of 1/x dx?

ln|x| + C

What is the integral of e^x dx?

e^x + C

What is the integral of a^x dx (for a>0, a≠1)?

a^x / (ln a) + C

What is the integral of 1/√(1-x^2) dx?

sin^-1 x + C

What is the integral of 1/(1+x^2) dx?

tan^-1 x + C

What is the integral of 1/(|x|√(x^2-1)) dx?

sec^-1 x + C