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How do you find the derivative of #(ln(x^(2)+3))^(3)#?

Answer 1

Charles Anctil

#(df)/(dx)=(6x(ln(x^2+3))^2)/(x^2+3)#

Here #f(x)=(g(x))^3#, where #g(x)=ln(h(x))# and #h(x)=x^2+3#

According to chain rule #(df)/(dx)=(df)/(dg)xx(dg)/(dh)xx(dh)/(dx)#

Hence #(df)/(dx)=3(ln(x^2+3))^2xx1/(x^2+3)xx2x#

= #(6x(ln(x^2+3))^2)/(x^2+3)#

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Answer 2

Scarlett Allison

To find the derivative of ((\ln(x^2 + 3))^3), you can use the chain rule. The derivative is (3(\ln(x^2 + 3))^2 \cdot \frac{d}{dx}(\ln(x^2 + 3))). Applying the derivative of (\ln(x^2 + 3)) with respect to (x), which is (\frac{1}{x^2 + 3} \cdot 2x), the final result is (3(\ln(x^2 + 3))^2 \cdot \frac{2x}{x^2 + 3}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.