If y = (5 - x)^{-3}, and \; dy/dx

Correct Answer is : 3(5 − x)4\; 3/(5\; -\; x)^4(5−x)43

Correct Answer is : 3(5 − x)4\; 3/(5\; -\; x)^4(5−x)43

Test Index

WAEC Further Mathematics 2019 Paper

Question : 31

Total: 39

If y = (5 - x)

^{-3}

\; \frac{dy}{dx}

Solution:

Concept:

Use the chain rule to differentiate a composite power function.

Explanation:

Given

y = (5 - x)^{-3}

Let

u = 5 - x

, so

y = u^{-3}

Then

\frac{du}{dx} = -1

and

\frac{dy}{du} = -3u^{-4}

By the chain rule:

\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}

\frac{dy}{dx} = (-3(5 - x)^{-4})(-1)

This simplifies to

3(5 - x)^{-4}

Therefore,

\frac{dy}{dx} = \frac{3}{(5 - x)^4}

Answer:

\frac{3}{(5 - x)^4}

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