Derivatives + Anti-derivatives to Memorize for Calc

Derivatives + anti-derivatives of trig + logarithmic functions. Good for Calc 🤩 For the purpose of the flashcards, integrals/anti-derivatives are denoted by the { symbol, and derivatives by d/dx.

d/dx(sin(x))

d/dx(sin(x))

cos(x)

d/dx(cos(x))

-sin(x)

d/dx(tan(x))

sec²(x)

d/dx(cot(x))

-csc²(x)

{cos(x)dx

sin(x)+C

{sin(x)dx

-cos(x)+C

{sec²(x)dx

tan(x)+C

{csc²(x)

-cot(x)+C

{sec(x)tan(x)dx

sec(x)+C

{csc(x)cot(x)dx

-csc(x)+C

d/dx(e^kx)

ke^kx

d/dx(lnx)

1/x

{(e^kx)dx

(1/k)e^kx+C

{(1/x)dx

lnx+C

d/dx(lnx)

xln(x)-x+C

d/dx(sin^-1x)

1/(1-x²)^1/2

d/dx(cos^-1x)

-1/(1-x²)^1/2

d/dx(tan^-1x)

1/(1+x²)

d/dx(sec^-1x)

1/(x(x²-1)^1/2

d/dx(csc^-1x)

-1/(x(x²-1)^1/2

d/dx(cot^-1x)

-1/(x²+1)