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**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:**

**Option A is incorrect.****Option B is incorrect.****C is correct.****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.****If you love our answers, you can login to comment and say hi to us at the comment section…**

**To raise new related question****s, c****lick the ASK A QUESTION BOTTON down this page…**

**/ culled from 2020 JAMB-UTME mathematics past question 27 /**