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

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Answer 1 · 2016-11-12T05:34:01

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

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

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