# How do you differentiate #f(x)=e^cosx#?

f you are studying maths, then you should learn the Chain Rule for Differentiation, and practice how to use it:

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To differentiate the function ( f(x) = e^{\cos(x)} ), you would use the chain rule. The chain rule states that if you have a composition of functions, the derivative is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

So, for ( f(x) = e^{\cos(x)} ):

[ f'(x) = \frac{d}{dx} \left( e^{\cos(x)} \right) = e^{\cos(x)} \times (-\sin(x)) ]

Therefore, the derivative of ( f(x) = e^{\cos(x)} ) is ( -e^{\cos(x)}\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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