Derivative of Cos x Square Using First Principle

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The formula to find derivative of a function f(x) using first principle :

Derivative of sinx using first principle :

Let

f(x) = cos(x²)

Sum to Product Trigonometric Identity,

In f'(x) above,

C = (x + h)²

D = x²

From standard results of limits,

Therefore,

[cos(x²)]' = 2xsin(x²)

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