Question
Asked Jun 27, 2019
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If fx)x3x+1 then fx)
(In x]3x
(3x+1}x3x
(2x+ In xr3x+ 1
3x13r 3 Inx
3x+13 In x
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If fx)x3x+1 then fx) (In x]3x (3x+1}x3x (2x+ In xr3x+ 1 3x13r 3 Inx 3x+13 In x

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Expert Answer

Step 1

Note:

Hi there! Thank you for posting the question. The first line in the image is not very clear. However, on comparing it with the below given options, we have found it logical to assume that the question enquires about f’(x). We are finding the derivative of the given function f(x).

Step 2

Obtain the derivative f’(x):

The given function is f(x) = x3x+1.

The derivative f’(x) is obtained as given below:

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f(x)xDifferentiate w.r.tx 3x+ d (x3-1);[Here, x=u(x) and 3x +1 vx) dx f'(x) _ By generalized power rule (In(s)x (3x +1)) ;| du(x) (x) 3x+1 = X f'(x)x31, In(u()v() X d X dx d dv du (uv) dx = ux +vX dx dx f'(x)x n(x)x 3x+1 In(x) dx (3x +1)+(3x +1) x. d (kx +k (kx)+-(k) dx and

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Step 3

Further calculation:

The derivative f’(x) is obtained as x3x+1[((3x+1)/x)+3ln(x)] from the cal...

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(kx)=kx dx dx d d d In(x)x 3x+1 = X -In (x) (3x +1)x dx (3x) (k)=0 f'(x) and dx dx d (In(x))= and dx 3x+1 (3 f'(x) (3x +1) 3 In(x) 3x+1 X X = (3x +1) 3r+1 = X 31n(x) +

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Calculus

Derivative

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