# How do you differentiate #g(x) =x (4x^6 + 5) # using the product rule?

According to the product rule, if

then

We can now locate that

and when the brackets are expanded,

By distributing the function and simply applying the power rule, you can verify the following answer:

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To differentiate ( g(x) = x(4x^6 + 5) ) using the product rule, you would apply the formula: [ (uv)' = u'v + uv' ] where ( u = x ) and ( v = 4x^6 + 5 ). Then, differentiate ( u ) and ( v ) individually. The derivative of ( u ) is ( u' = 1 ), and the derivative of ( v ) is ( v' = 24x^5 ). Finally, apply the product rule formula to find ( g'(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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