How do you find f" given $f(x)= (6x + 5)^(1/3)$ ?

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Answer 1 · 2016-08-29T17:46:28

$f''(x)=-8/(6x+5)^(5/3)$ .

$f(x)=(6x+5)^(1/3)$

$rArr f'(x)=1/3*(6x+5)^(1/3-1)*d/dx(6x+5)............["Chain Rule"]$

$=6/(3(6x+5)^(2/3))$

$f'(x)=2/(6x+5)^(2/3)$

Now, $f''(x)={f'(x)}'$

$:. f''(x)=2(-2/3)(6x+5)^(-2/3-1)*6$

$:. f''(x)=-8/(6x+5)^(5/3)$ .

How do you find f" given f(x)= (6x + 5)^(1/3)f(x)= (6x + 5)^(1/3)?