Derivatives of Common Functions

d/dx(xⁿ)

n*x^n-1

d/dx(e^x)

e^x

d/dx(a^x)

a^x * ln(a)

d/dx(log_b(x))

1/x * ln(b)

d/dx(ln|x|)

1/x

d/dx(sin(x))

cos(x)

d/dx(cos(x))

-sin(x)

d/dx(tan(x))

sec²(x)

d/dx(csc(x))

-csc(x)cot(x)

d/dx(sec(x))

sec(x)tan(x)

d/dx(cot((x))

-csc²(x)

d/dx(sin^-1(x))

1/sqrt(1-x^2)

d/dx(tan^-1(x))

1/(1+x^2)

d/dx(cos^-1(x))

-1/sqrt(1-x^2)

d/dx[csc^-1(x)]

-1/|x|sqrt(x^2-1)

d/dx[sec^-1(x)]

1/|x|√x^2-1

d/dx[cot^-1(x)]

1/(1+x^2)