# How do you differentiate #g(x)=cos(10^(2x))#?

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To differentiate ( g(x) = \cos(10^{2x}) ), you can use the chain rule. The derivative of cosine is negative sine, and the derivative of the exponent ( 10^{2x} ) with respect to ( x ) involves the natural logarithm of the base multiplied by the function itself, then multiplied by the derivative of the exponent. So, the derivative of ( g(x) ) is:

[ g'(x) = -\sin(10^{2x}) \cdot \ln(10) \cdot 10^{2x} \cdot 2 ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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