Question

How do you find the derivative of `f(x) = 5+ 3x + 6x^2+ 7x^3`?

Answer 1

`f'(x)=3 + 12x + 21x^2`

Explanation:

Differentiating `f(x)` is determined by applying the sum of
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differentiation and the power rule.
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Sum of differentiation :
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`(u(x)+v(x))'=(u(x))'+(v(x))'`
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Power Rule Differentiation:

`(d(x^n))/dx=nxxx^(n-1)` `" "n in ZZ`

`f'(x) = (5)' + (3x)' + (6x^2)' + (7x^3)'`
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`f'(x)= 0 + 3 + (6xx2)x + (7xx3x^2)`
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`f'(x)=3 + 12x + 21x^2`