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# Find the derivative of the function y = 2x²(2x – 1) at the point x = -1

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**Find the derivative of the function y = 2x²(2x – 1) at the point x = -1?**

**A.**** 18**

**B.**** 16**

**C.**** -4**

**D.**** -6**

**QUICK ANSWER…**

**B**

**DETAILS…**

**The derivative of the function y = 2x²(2x – 1) at the point x = -1**** is equal to 16.**

**If y**** = 2x²(2x – 1)****,**

**dy/dx can be determined using product rule.**

**Splitting the function into two,**

**Let u = 2x², and v = (2x – 1).**

**du/dx = 4x**

**dv/dx = 2**

**now product rule states thus:**

**dy/dx = vdu/dx + udv/dx**

**dy/dx = (2x – 1)(4x) + (2x²)(2)**

**dy/dx = 8x² – 4x + 4x²**

**dy/dx = 12x² – 4x**

**at point x = -1, we have:**

**dy/dx = 12(-1)² – 4(-1)**

**dy/dx = 12 + 4**

**dy/dx = 16**

**Now for the right answer to the above question:**

**Option A is incorrect.****Option B is correct.****C is not correct.****D is not the correct answer.**

**KEY-POINTS…**

**You may please note these/this:**

**When two simple functions are combined as in the case of this question, use the product rule to differentiate.****Product rule →****dy/dx = vdu/dx + udv/dx.**

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**/ culled from 20****21**** JAMB-UTME**** MATHEMATICS**** question**** 8 ****/**