# How do you differentiate #f(x) = (2 x^2 +5 x +10)^cos(x)#?

Then

Differentiating both sides, using the chain rule on the left and the product rule on the right:

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To differentiate ( f(x) = (2x^2 + 5x + 10)^{\cos(x)} ), we use the chain rule. The derivative is given by ( f'(x) = \cos(x)(2x^2 + 5x + 10)^{\cos(x)-1} \cdot (4x + 5) - (2x^2 + 5x + 10)^{\cos(x)} \cdot \ln(2x^2 + 5x + 10) \cdot \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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