derivative of y=3+(12)/(2-x) — step-by-step solution

We save the definition:

y = 3 + \frac{12}{2 - x}

To ease differentiation, the expression

\frac{12}{2 - x}

is turned into

12 \cdot {(2 - x)}^{-1}

Let's perform the differentiation:

\frac{d}{d x} (3 + 12 \cdot {(2 - x)}^{-1})

0 + \frac{d}{d x} (12 \cdot {(2 - x)}^{-1})

Apply the differentiation rule:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{(n - 1)}

with f =

2 - x

12 \cdot (-1 \cdot \frac{d}{d x} (2 - x) \cdot {(2 - x)}^{-2})

ℹ

12 \cdot (-1)

-12

‖

\frac{d}{d x} (2 - x)

0 + \frac{d}{d x} (- x)

-12 \cdot (0 + \frac{d}{d x} (- x)) \cdot {(2 - x)}^{-2}

- \frac{12 \cdot \frac{d}{d x} (- x)}{{(2 - x)}^{2}}

- \frac{12 \cdot (-1)}{{(2 - x)}^{2}}

- \frac{-12}{{(2 - x)}^{2}}

▶Derivative:

\frac{12}{{(2 - x)}^{2}}