If y = (1 – 2x)³, find the value of dy/dx at x = -1

A. 27

B. -6

C. -54

D. 54

QUICK ANSWER…

C

DETAILS…

We will differentiate this by substitution method as follows:

y = (1 – 2x)³

let (1 – 2x) be = u,

therefore,

y = u³ and

du/dx = -2

dy/du = 3u²

for this function of function, the derivative will be:

dy/dx = dy/du × du/dx

dy/dx = 3u² × -2 = -6u²

recall that earlier, we assumed u = 1 – 2x, hence:

dy/dx = -6(1 – 2x)²

finally, substituting x = -1 into this, we have:

dy/dx = -6(1 – 2x)²

dy/dx = -6(1 – 2(-1))²

dy/dx = -6(1 + 2)²

dy/dx = -6(3)²

dy/dx = -6 × 9 = – 54

Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is incorrect.
3. C is correct.
4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

• Questions like this can be differentiated through expanding the polynomial (1 – 2x)³, and then differentiating each component. But this will take time.
• Substitution method as done above is the quickest method to apply.
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/ culled from 2020 JAMB-UTME mathematics past question 27 /