Question

Differentiate the given function:

lnx^3
should the next step be 3lnx^2

Answer 1

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.

Answer 2

good answer apples

Answer 3

ln(x) dresses down to 1/x:

3ln(x)^2
-------
x

Answer 4

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 \[\frac{3}{x}\]

Answer 5

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

Answer 6

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