29 terms

Formula for the Derivative by the Limit Process

f'(x)=lim ∆x→0[(f(x+∆x)-f(x))/(∆x)]

Point-Slope Formula

y - y₁=m(x - x₁)

The derivative of a constant is always = _____

0

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

f'(x) + g'(x)

Difference Rule: d/dx[f(x) - g(x)]=

f'(x) - g'(x)

Power Rule: d/dx[ xⁿ]=

nx^(n-1)

The derivative of position is

Velocity

The derivative of velocity is

Acceleration

s(t) usually represents

Position

s'(t) usually represents

Velocity

s''(t) usually represents

Acceleration

v₀ represents

Initial velocity (starting velocity)

s₀

Initial height (starting height)

d/dx[sin(x)]=

cos(x)

d/dx[cos(x)]=

-sin(x)

d/dx[tan(x)]=

sec²(x)

d/dx[sec(x)]=

sec(x)tan(x)

d/dx[csc(x)]=

-csc(x)cot(x)

d/dx[cot(x)]=

-csc²(x)

Product Rule (Mnemonic)

1D2+2D1

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

f(x)g'(x)+g(x)f'(x)

Quotient Rule (Mnemonic)

LowDHi-HiDLow over the square of what's below

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

[g(x)f'(x)-f(x)g'(x)]/g(x)²

Chain Rule: d/dx[f(u)]=

f'(u)u'

Chain Rule: d/dx[f(g(x))]=

f'(g(x))g'(x)

As you take a derivative of y with respect to x, you have to multiply the derivative by ________

dy/dx

In implicit differentiation, we multiply by dy/dx because of the _________ rule

Chain

d²y/dx² means to find the __________ ____________

Second Derivative

If a graph of an equation has a horizontal tangent line (slope of zero), then the graph of its derivative should cross the ___-_______ at that point

x-axis