# How do you calculate the derivative of #d/dx∫sin^2tdt# from 0 to x?

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To calculate the derivative of ( \frac{d}{dx} \int_{0}^{x} \sin^2(t) , dt ), you apply the Fundamental Theorem of Calculus and the Chain Rule. The derivative is equal to the integrand evaluated at the upper limit multiplied by the derivative of the upper limit, which is ( 1 ). So, the derivative is ( \sin^2(x) ).

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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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