Key Equations

(M6-1)

Y = a + b X

$Y = a + b X$

Equation of a straight line.

(M6-2)

b = \frac{Change in Y}{Change in X} = \frac{Δ Y}{Δ X} = \frac{Y_{2} - Y_{1}}{X_{2} - X_{1}}

$b = \frac{Change in Y}{Change in X} = \frac{Δ Y}{Δ X} = \frac{Y_{2} - Y_{1}}{X_{2} - X_{1}}$

Slope of a straight line found from two points.

(M6-3)

Y' = \frac{d Y}{d X} = lim_{Δ X \to 0} {\frac{Δ Y}{Δ X}}

$Y' = \frac{d Y}{d X} = lim_{Δ X \to 0} {\frac{Δ Y}{Δ X}}$

Definition of derivative.

(M6-4)

If Y = c where c is any constant, then Y' = 0

$If Y = c where c is any constant, then Y' = 0$

Derivative of a constant function.

(M6-5)

If Y = X^{n}, then Y' = n X^{n - 1}

$If Y = X^{n}, then Y' = n X^{n - 1}$

Derivative of X raised to a power.

(M6-6)

If Y = c X^{n}, then Y' = c n X^{n - 1}

$If Y = c X^{n}, then Y' = c n X^{n - 1}$

Derivative of a constant times a function of X.

(M6-7)

If Y = 1 / X^{n}, then Y' = - n X^{- n - 1} = - n / X^{n + 1}

$If Y = 1 / X^{n}, then Y' = - n X^{- n - 1} = - n / X^{n + 1}$

Derivative of $1 / X$ $1 / X$ to a power.

(M6-8)

If Y = g (x) + h (x), then Y' = g' (x) + h' (x)

$If Y = g (x) + h (x), then Y' = g' (x) + h' (x)$

Derivative of the sum of two functions of X.

(M6-9)

If Y = g (x) - h (x), then Y' = g' (x) - h' (x)

$If Y = g (x) - h (x), then Y' = g' (x) - h' (x)$

Derivative of the difference of two functions of X.

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Table of Contents for Key Equations