Calc 1 Theorems and Identities

Derivative of a Constant Function

The slope of a constant value is always 0

d/dx (c ) = 0

Derivative of a Power Function

f(x) = xⁿ

d/dx(xⁿ) = nx^n-1

The Derivative Constant Multiple Rule

d/dx [c(f(x))] = c * d/dx f(x)

The Derivative Sum Rule

d/dx [f(x)+g(x)] = d/dx f(x) + d/dx g(x)

Derivative of Natural Exponential Function

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

Derivative Product Rule

1st * d 2nd + 2nd * d 1st

d/dx [f(x)g(x)] = f(x) d/dx g(x) + g(x) * d/dx f(x)

Derivative Quotient Rule

low d high - high d low all over low²

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

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)