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)#