# How do you differentiate #f(x)=xsinx+cosx#?

Separating the initial f(x)

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To differentiate the function ( f(x) = x \sin(x) + \cos(x) ), you would use the product rule and the chain rule. The product rule states that if you have two functions, say ( u(x) ) and ( v(x) ), then the derivative of their product ( u(x)v(x) ) is given by ( u'(x)v(x) + u(x)v'(x) ). Applying this rule to ( x \sin(x) ), you get ( (1)(\sin(x)) + (x)(\cos(x)) ). Then, the derivative of ( \cos(x) ) is ( -\sin(x) ). So, the derivative of ( f(x) ) with respect to ( x ) is ( \sin(x) + x \cos(x) - \sin(x) ), which simplifies to ( x \cos(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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