How do you differentiate #f(x)=4x^5-5x^4# using the sum rule?

Answer 1

#20x^4-20x^3# or #20x^3(x-1)#

Given: #f(x)=4x^5-5x^4#.
The sum rule for differentiation states that #d/dx(f(x)+-g(x))=f'(x)+-g'(x)#
#:.f'(x)=(4x^5)'-(5x^4)'#
Now, we use the power rule, which states that, #d/dx(na^x)=nxa^(x-1),x!=-1#.

And so, we get:

#f'(x)=5*4x^4-4*5x^3#
#=20x^4-20x^3#

We can factor this into:

#=20x^3(x-1)#
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Answer 2

To differentiate ( f(x) = 4x^5 - 5x^4 ) using the sum rule, you differentiate each term separately and then add them together.

[ \frac{{d}}{{dx}}(4x^5) = 4 \times 5x^{5-1} = 20x^4 ] [ \frac{{d}}{{dx}}(-5x^4) = -5 \times 4x^{4-1} = -20x^3 ]

So, ( \frac{{d}}{{dx}}(4x^5 - 5x^4) = 20x^4 - 20x^3 ).

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Answer from HIX Tutor

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.

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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