Question

f(х)=х⁵-7х³+5х
f(х)=5х⁴-4х³+3х²-2
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Answer 1

$a)f(x) = {x}^{5} - 7 {x}^{3} + 5x \\ f'(x) = ( {x}^{5} - 7 {x}^{3} + 5x)' \\ f'(x) =5 {x}^{4} - 21 {x}^{2} + 5$

$b)f(x) = (5 {x}^{4} - 4 {x}^{3} + 3 {x}^{2} - 2) \\ f'(x) = (5 {x}^{4} - 4 {x}^{3} + 3 {x}^{2} - 2)' \\ f'(x) = 20 {x}^{3} - 12 {x}^{2} + 6x$

$f(x) = {x}^{n} \\ f '(x) = n {x}^{n - 1}$

$f(x) = c, \: c = const \\ f'(x) = 0$