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Question

How do you differentiatey=logx2?


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Solution

Step 1: Differentiate the function :

We have to differentiate y=logx2 using the chain rule, which states that ddxfgx is f'gx×g'x where fx=logx and gx=x2.

Let us consider, u as x2.

dduloguddxx2

The derivative of logu with respect to u is 1uln10.

1uln10·ddxx2

Replace u with x2.

1x2ln10ddxx2

Step 2: Differentiate the above equation.

Differentiating using the Power Rule which states that ddxxn is nx-1, where n=2.

1x2ln102x

2xx2ln10

x·2x2ln10

Therefore,

dydx=2xln10

Hence, the differentiate value of y=logx2 is 2xln10.


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