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

Monday, November 5, 2012

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

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( $\displaystyle{{x}}^{{{3}}}$ + 1 ) and v(x) =
$\displaystyle{{x}}^{{{3}}}$ + 1

f'(x) = [ln( $\displaystyle{{x}}^{{{3}}}$ + 1)]'*( $\displaystyle{{x}}^{{{3}}}$ +
1)'

f'(x) = [1/( $\displaystyle{{x}}^{{{3}}}$ + 1)]*(3 $\displaystyle{{x}}^{{{2}}}$
)

The requested derivative of the given
function is f'(x) = 3 $\displaystyle{{x}}^{{{2}}}$ /( $\displaystyle{{x}}^{{{3}}}$ + 1).

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