{Differentiate } f(x) = 1/(1 - x²)^5 with respect to x.

Correct Answer is : 10x(1−x2)610x/(1-x²)^6(1−x2)610x

Correct Answer is : 10x(1−x2)610x/(1-x²)^6(1−x2)610x

Test Index

WAEC Further Mathematics 2023 Paper

Question : 14

Total: 40

\text{Differentiate } f(x) = \frac{1}{(1 - x^2)^5}

x

Solution:

Concept:

Rewrite the expression as a power of

u

and apply the chain rule.

Explanation:

Write

f(x)

(1 - x^2)^{-5}

Let

u = 1 - x^2

, so

f(u) = u^{-5}

Then

\frac{du}{dx} = -2x

and

\frac{df}{du} = -5u^{-6}

By the chain rule,

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

Therefore,

\frac{df}{dx} = (-5u^{-6})(-2x) = 10x\,u^{-6}

Substitute

u = 1 - x^2

to get

\frac{df}{dx} = 10x(1-x^2)^{-6}

So,

f'(x) = \frac{10x}{(1-x^2)^6}

Answer:

\frac{10x}{(1-x^2)^6}

, which is Option D.

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