Question

find dy/dx if y=√1+ln³(x)
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Answer 1

Answer:

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-3ln^2(x)[2+ln^3(x)]/2

Step-by-step explanation:

let 1+ln^3(x) be z

so, differentiation of z will be

0+3ln^2(x)=dx/dx

so,3ln^2(x)=dz/dx......(1)

now, differentiate y=√1+z

dy/dz=-1/2(1+z) ......(2)

now multiply (1)&(2)

so,dy/dx=-3ln^2(x)[1+z]/2

now, substitute z as 1+ln^3(x)

so,dy/dx= -3ln^2(x)[2+ln^3(x)]/2