Question

(2)Please determine : FIRST: (A) W’(X) ; THEN: (B) W’(0); W(X) IS DEFINED BELOW:
W(X) = [ (10* (X^4) ) – 8 ] * { [ (30*X ) + 25 ] ^ (0.5) }
HOWEVER, YOU MUST USE LOGARITHMIC DIFFERENTIATION, NOT THE PRODUCT RULE; IMPORTANT NOTE : YOU WI LL NOT BE GIVEN A N Y CREDIT FOR USE OF THE PRODUCT RULE, IN ORDER TO OBTAIN THE DERIVATIVE OF T(X) !
SERIOUSLY – YOU M U S T USE O N L Y LOGARITHMIC DIFFERENTIATION HERE !
HINT: (A) FIRST , TAKE “ Ln “ of BOTH SIDES; THEN, DIFFERENTIATE IMPLICITLY, PARTLY WITH USE OF THE CHAIN RULE; THEN, SOLVE FOR W’(X). FINALLY, PLEASE
ALSO remember to EVALUATE W’(X) at X =0, to complete YOUR PART (B) WORK !

Answer 1

Given,

We need to find out W'(x) using logarithmic differentiation.

Let us take ln in both the side of the equation.

Or,or,

Or, Now differentiating both side with respect to x.

Or, or,

Or,

Or,

or,taking L.C.M in the right hand side of the equation

or,

Or,

Above is the simplified form of W'(x) in terms of x.

Now we need to find W'(0)

Therefore W'(0) would be,

W'(0)= -120/√25

Or,W'(0) = -120/5 = -24

Thus putting 0 in the equation of W'(x) we can easily find out W'(0).