anonymous 5 years ago Differentiate the given function: lnx^3 should the next step be 3lnx^2

1. apples

Well, note that here you would use the chain function. The outer function is log(x) and the inner function is x^3. Noting that $\frac{d}{dx} \left(f(g(x))\right) = f'(g(x)) \cdot g'(x)$ then you'll want to differentiate log(x) and plug x^3 into it, then multiply that by the derivative of x^3.

2. anonymous

3. amistre64

ln(x) dresses down to 1/x: 3ln(x)^2 ------- x

4. apples

That's not correct. You're right that d/dx log(x) = 1/x, however this yields the result $\frac{1}{x^3} \cdot 3x^2$ which simplifies to $\frac{3}{x}$

5. anonymous

if you mean (lnx)^3 then amistre is right if you mean ln(x^3) then apples is right

6. amistre64

...... oh the humanity!! ;)