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)#.