math

What is the derivative of sin(u)?

d/dx[sin(u)] = (cos(u))u′

What is the derivative of cos(u)?

d/dx[cos(u)] = -(sin(u))u′

What is the derivative of tan(u)?

d/dx[tan(u)] = (sec²(u))u′

What is the derivative of cot(u)?

d/dx[cot(u)] = -(csc²(u))u′

What is the derivative of sec(u)?

d/dx[sec(u)] = (sec(u)tan(u))u′

What is the derivative of csc(u)?

d/dx[csc(u)] = -(csc(u)cot(u))u′

What is the derivative of arcsin(u)?

d/dx[arcsin(u)] = u′/(√(1−u²))

What is the derivative of arccos(u)?

d/dx[arccos(u)] = -u′/(√(1−u²))

What is the derivative of arctan(u)?

d/dx[arctan(u)] = u′/(1+u²)

What is the derivative of arccot(u)?

d/dx[arccot(u)] = -u′/(1+u²)

What is the derivative of arcsec(u)?

d/dx[arcsec(u)] = u′/|u|√(u²−1)

What is the derivative of arccsc(u)?

d/dx[arccsc(u)] = -u′/|u|√(u²−1)

What is the integral of 1/(a²−u²) du?

∫ 1/(a²−u²) du = arcsin(u/a) + C

What is the integral of 1/(a²+u²) du?

∫ 1/(a²+u²) du = (1/a)arctan(u/a) + C

What is the integral of 1/(u√(u²−a²)) du?

∫ 1/(u√(u²−a²)) du = (1/a)arcsec(|u/a|) + C