# Math 3A Midterm 2

Derivative of a Constant

(c)′ = 0

Acceleration

The time derivative of velocity

Derivative of ln(x)

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

Velocity

The time derivative of position

Derivative of tan−1(x)

(d/dx)tan−1(x)′ = 1/(1+x^2)

Derivative of sin−1(x)

(d/dx)sin−1(x) = 1/√(1−x^2)

Chain Rule

(d/dx)f(g(x)) = f′(g(x))g′(x)

Derivative of cos(x)

cos(x)′ = − sin(x)

Product Rule

(fg)′ = f′g + g′f

Derivative of sin(x)

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

limx->0 (sin(x)/x)

1

Derivative of a^x

(d/dx)ax = ln(a)(a^x)

Derivative of e^x

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

The Number e

The real number such that limh→0 (e^h−1)/h = 1

Additivity Rule (A.K.A. Sum Rule)

(d/dx)f + g = f′+g′

Constant Multiple Rule

(cf)′ = cf′

Power Rule

(d/dx)x^n = nx^(n−1)

Area of a Triangle

A = (½)bh

Area of a Rectangle

A = bh

Area of a Trapezoid

A = ((b1+b2)/2)h

Volume of a Sphere

V=(4/3)π(r^3)

Volume of a Cylinder

V=π(r^2)h

Volume of a Prism

base*height

Surface area of a Sphere

SA=4π(r^2)

Surface area of a Cylinder

SA=2πrh+2π(r^2)

Derivative of tan(x)

sec^2(x)

Derivative of cot(x)

-csc^2(x)

Derivative of csc(x)

-csc(x)cot(x)

Derivative of sec(x)

sec(x)tan(x)