Common Derivatives & Integrals

d/dx (C) =

0

d/dx (x) =

1

d/dx (cx) =

C

d/dx (xⁿ) =

nx^n-1

d/dx (cxⁿ) =

ncx^n-1

d/dx [a^x] =

a^x ln(a)

d/dx [e^x] =

e^x

d/dx [lnx] =

1/x,   x > 0

d/dx [lnx] =

1/x, x ≠ 0

d/dx [Log_a(x)] =

1 / xln(a), x > 0

∫ dx =

x + C

∫k dx =

kx + C

∫n^x dx =

∫n^-x dx =

∫1/x dx =

ln|x| + C

∫x^-1 dx

ln|x| + C

 

∫e^u du =

e^u + C

∫ a^u du =