What is derivative of f(x)=ln(x^3+1)?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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Since the function f(x) is a result of composing two functions, w'ell have to use the chain rule to find out the derivative of f(x).

f(x) = u(v(x))

f'(x) = u'(v(x))*v'(x)

Let u(v(x)) = ln(`x^(3)`+ 1 ) and v(x) = `x^(3)` + 1

f'(x) = [ln(`x^(3)` + 1)]'*(`x^(3)` + 1)'

f'(x) = [1/(`x^(3)` + 1)]*(3`x^(2)` )

The requested derivative of the given function is f'(x) = 3`x^(2)` /(`x^(3)` + 1).

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