Calc

Derivative of x^n

d/dx(x^n) = n * x^(n−1)

Derivative of ln(x)

d/dx(ln(x)) = 1/x

Derivative of e^x

d/dx(e^x) = e^x

Derivative of b^x

d/dx(b^x) = b^x ln(b)

Derivative of sin(x)

d/dx(sin(x)) = cos(x)

Derivative of cos(x)

d/dx(cos(x)) = -sin(x)

Derivative of tan(x)

d/dx(tan(x)) = sec^2(x)

Derivative of sec(x)

d/dx(sec(x)) = sec(x) tan(x)

Derivative of csc(x)

d/dx(csc(x)) = -csc(x) cot(x)

Derivative of cot(x)

d/dx(cot(x)) = -csc^2(x)

Derivative of arctan(x)

d/dx(tan^−1(x)) = 1/(x^2 + 1)

Integral of 1/x^n

∫1/x^n dx = (1/n + 1)x^(n + 1) + C (n ≠ -1)

Integral of e^(ax)

∫e^(ax) dx = (1/a)e^(ax) + C

Integral of cos(ax)

∫cos(ax) dx = (1/a)sin(ax) + C

Integral of sin(ax)

∫sin(ax) dx = -(1/a)cos(ax) + C

Integral of sec^2(x)

∫sec^2(x) dx = tan(x) + C

Integral of csc^2(x)

∫csc^2(x) dx = -cot(x) + C

Identity: sin^2(x) + cos^2(x)

sin^2(x) + cos^2(x) = 1

Identity for tan^2(x) + 1

tan^2(x) + 1 = sec^2(x)