derivative of g(x)=(x^2-64)/(x+8)

We save the definition:

g (x) = \frac{x^{2} - 64}{x + 8}

Let's differentiate:

\frac{d}{d x} (\frac{x^{2} - 64}{x + 8})

By using the formula:

a^{2} - b^{2} = (a - b) \cdot (a + b)

, we divide the numerator and denominator of

\frac{x^{2} - 64}{x + 8}

by the common factor:

x + 8

, which gives the new expression:

x - 8

\frac{d}{d x} (x - 8)

ⓘ The derivative of a sum is the sum of the derivatives:

\frac{d}{d x} (x - 8)

1 + 0

1 + 0

ⓘ Adding 0 changes nothing:

1 + 0

1

▶Derivative:

1