# How do you differentiate #y = x^2(sinx)^4 + x(cosx)^-2#?

You can try simplifying this, but I don't think there's much to simplify.

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To differentiate the function y = x^2(sin(x))^4 + x(cos(x))^(-2), you would apply the product rule and chain rule.

The derivative would be:

y' = 2x(sin(x))^4 + x^2(4(sin(x))^3(cos(x))(cos(x)) - 2x(cos(x))^(-3)(-sin(x)))

Simplified, this becomes:

y' = 2x(sin(x))^4 + 4x^2(sin(x))^3(cos(x))^2 + 2x(cos(x))^(-3)sin(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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