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

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Answer 1 · 2018-04-27T07:16:31

$20x^4-20x^3$ 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:

$=20x^3(x-1)$

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