# How do you differentiate #f(x)= (2 x^2 + 7 x - 2)/ (x cos x )# using the quotient rule?

See below.

This will also require a use of the product rule for the function in the denominator.

You can then simplify as required.

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The given equation is

We use the formula for derivative of rational expression

We simplify at this point

God bless....I hope the explanation is useful.

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To differentiate ( f(x) = \frac{2x^2 + 7x - 2}{x \cos(x)} ) using the quotient rule, you can apply the formula:

[ f'(x) = \frac{g(x) \cdot f'(x) - f(x) \cdot g'(x)}{[g(x)]^2} ]

Where ( f(x) = 2x^2 + 7x - 2 ) and ( g(x) = x \cos(x) ). Then, find the derivatives of ( f(x) ) and ( g(x) ) separately and substitute into the formula.

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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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