Basic Derivatives

f(x) = x

f(x) = x

dy/dx = 1

f(x) = x^2

dy/dx = 2x

f(x) = cos(x)

dy/dx = -sin(x)

f(x) = sin(x)

dy/dx = cos(x)

f(x) = tan(x)

dy/dx = sec^2(x)

f(x) = csc(x)

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

f(x) = sec(x)

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

f(x) = cot(x)

dy/dx = -csc^2(x)

f(x) = x^3

dy/dx = 3x^2

f(x) = x^4

dy/dx = 4x^3

f(x) = e^x

dy/dx = e^x

f(x) = e^(2x)

dy/dx = 2(e^(2x))

f(x) = ln(x)

dy/dx = 1/x

f(x) = ln(2x)

dy/dx = 2/x

f(x) = log₁₀(x)

dy/dx = 1/((x)(ln(10))

f(x) = 2^x

dy/dx = (2^x)(ln(2))

f(x) = 2^(2x)

dy/dx = 2(2^x)(ln(2))

Power Rule

dy/dx (x^n) = n(x^(n-1))

Product Rule

dy/dx (f•g) = f • dy/dx(g) + g • dy/dx(f)

Quotient Rule

dy/dx(f/g) = ((g)•d(f) - (f)d(g))/(g^2)