Derivatives & integrals

constant rule

d/dx c = 0

constant multiple rule

d/dx[cf(x)]=cf’(x)

sum rule

d/dx[f(x)+g(x)] = f’(x)+g’(x)

difference rule

d/dx[f(x) - g(x)] = f’(x) -g’(x)

product rule

d/dx[f(x)g(x)] = f’(x)g(x)+g’(x)f(x)

quotient rule

d/dx [f(x)/g(x)] = [g(x)f’(x) - f(x)g’(x)]/[g(x)]²

chain rule

d/dx [f(g(x))] = f’(g(x))g’(x)

power rule

d/dx lxⁿl = nx^n-1

d/dx[sin(x)]

cosx

∫cosx dx

sinx + c

d/dx[cos(x)]

-sinx

∫-sinx dx

cosx + c

d/dx[tan(x)]

sec²x

∫sec²x dx

tan(x) + c

d/dx[csc(x)]

-csc(x)cot(x)

∫-csc(x)cot(x) dx

csc(x) + c

d/dx[sec(x)]

sec(x)tan(x)

∫sec(x)tan(x) dx

sec(x) + c

d/dx[cot(x)]

-csc²(x)

∫-csc²(x) dx

cotx + c

d/dx sin^-1(x)

1/sqrt(1-x²)

∫1/sqrt(1-x²) dx

sin^-1(x) + c

d/dx cos^-1(x)

-1/sqrt(1-x²)

∫-1/sqrt(1-x²) dx

cos^-1(x) + c

d/dx tan^-1(x)

1/(1-x²)

∫1/(1-x²) dx

tan^-1(x) + c

d/dx csc^-1(x)

-1/(lxlsqrt(x²-1))

∫-1/(lxlsqrt(x²-1)) dx

csc^-1(x) + c

d/dx sec^-1(x)

1/(lxlsqrt(x²-1))

∫1/(lxlsqrt(x²-1)) dx

sec^-1(x) + c

d/dx cot^-1(x)

-1/(1+x²)

∫-1/(1+x²) dx

cot^-1(x) + c

d/dx [e^x]

e^x

∫e^x dx

e^x + c

d/dx [a^x]

a^xln(a)

∫a^xln(a) dx

a^x + c

d/dx [ln(x)]

1/x

∫1/x dx

ln(x) + c

d/dx [log_a(x)]

1/[x*ln(a)]

∫1/[x*ln(a)] dx

log_a(x) + c