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Asked Oct 30, 2019
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(c) f(x) = x
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(c) f(x) = x

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|6. Find the derivative of the following functions using logarithmic differentiation.
x(x+2)
(2x+1) (3+2)
(a) f(x)
(2r1)(422)x - 9
(b) f(x)
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|6. Find the derivative of the following functions using logarithmic differentiation. x(x+2) (2x+1) (3+2) (a) f(x) (2r1)(422)x - 9 (b) f(x)

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Expert Answer

Step 1

take log on both side and using the property.

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x(x+2) we have given f(x), V(2x+1)(3x+2) 71/2 x(x+2) x(x+2) let f(x) y or y (2x+1)(3x+2) (2x+1)(3x+2) x(x+2) (2x+1)(3x+2) take log on both side we get: logy-log 2 log(m/n)=logm-logn) or logylogx(x+2)-log(2x+1)(3x+2)] (log(mxn)-logm+logn) 1 or logylogx+log(x+2)-log(2x+1)-log(3x+2)]

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Step 2

differentiation of logarithmic function.

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now differentiate both side we get: 1 dy 1 2 3 dx 2 x (x+2) (2x+1) (3x+2) У dy_y 1 dx 2x (х+2) (2x+1) (3х+2) 2 1 3 or now put the value of y we get: x(х+2) dy_V(2x+1)(3x+2) 1 1 + 2 3 х (x+2) (2х+1) (3x+2). dx 2

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Step 3

take log on both side and u...

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b)we have the function f(x)-y-(2x+1)(4x)(x-9) take log on both side we get: logy=log(2x+1)(4x)(Vx-9)=log(2x+1)+log(4x2)+log(x-9)

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Math

Calculus