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Questions & Answers

How do I differentiate sin^2(x)?

In order to understand the differentiation of this function, it is advised to use the Chain Rule. Why Chain Rule? Because Chain Rule allows you to break down the differentiation steps, which makes it easier for you to understand how you reached the final derivative.

Chain Rule Formula:

dy/dx= dy/du × du/dx

Step 1: Assume

y= sin²(x)

Step 2: Assume 

u= sin(x)

Step 3: Replace the sinx with u in the original equation

y= u²

Step 4: Differentiate u with respect to x

du/dx= cos(x)

Step 5: Differentiate y with respect to u

dy/du= 2u

Step 6: Replace the u with sin(x) 

dy/du= 2sin(x)

Step 7: Substitute step 4 and step 6 in the chain rule

dy/dx= dy/du × du/dx

dy/dx= 2sin(x) × cos(x)

dy/dx= 2sin(x)cos(x)

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