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Use logarithmic differentiation to find the derivative of y with respect to the independent variable. y = (In x) Inx O In (Inx) +1 X O In (Inx) + 1 (In x) In x X O In x In (In x) O ( In xin x XFind the derivative of the function. y = 4 In sin 2 5x In sin 5x O 40 sin 5x O 40 cot 5x O 10 tan 5xUse logarithmic differentiation to find the derivative of y with respect to the independent variable. y = (cos x) * (cos x)* (In cos x - x tan x) (cos x)* (In cos x + x cot x) In x(cos x)* - 1 O In cos x - x tan xUse logarithmic differentiation to find the derivative of y. y = COS X 413x + 8 COs X 13x + 8 Incos x + In( 3x + 8) O 3 Cos x 13x + 8 -tank + 2(3x + 8) O 3 COS X 13x + 8 + sinx . Coxx 3x + 8 O -6-tanx - 13-tanx 3x + 16Evaluate the integral. 6 + 1x47 dx X 1 + C O + 1 In 6 OA Use L'Hopital's rule to find the limit. O N|UI csc 10x O lim X-7/2 CSC 4x UIN NUI ' O OUse L'Hopital's rule to find the limit. lim x 1/(13x - 13) O -1/13 O e O ( 14 O 2/13Use logarithmic differentiation to find the derivative of y with respect to the independent variable. y = x In x O xIn x - 1x O O 2 O 2xIn x - 1InxFind the derivative of y with respect to the independent variable. y = 7 cos ne O -n/cos ne In 7 sin ne O 7cos ne In 7 sin ne O n/cos ne In 7 O 7cos neFind the value of df1 /dx at x = f(a). f(x) = 5x + 10, a = 2 O O O O 10Evaluate the integral. 4e(4 sin 2x) dx sec 2x O In( sec 2x) + C O (4 sin 2x) + C O 4 In( sec 2x) + C O 1 (4 sin 2x) + CFind an equation of the line tangent to the given curve at the point (a, f(a)). f(x) = 7e -3%, a= 0 Oy = 7x+7 Oy = 3x - 7 Oy=-21x +7 O y = 21x - 7Find the derivative of y with respect to x, t, or 0, as appropriate. y = In 3x 2 O 1 2x + 3 O XIN ZIG O O 2x x2+3Find the derivative of y with respect to x, t, or 0, as appropriate. y = In 9x O 1 9x O 1 9x O 1 X OUse L'Hopital's rule to find the limit. ex - 1 lim x-0 sin 9x O 1 9 O O 1Use L'Hopital's rule to find the limit. lim x 1/(12x - 12) x-1 O 2/12 O 1/12 O - 13 OeFind the limit. lim x -5/In x x -0+ O\fA Use L'Hopital's rule to find the limit. ex - 1 lim x-0 sin 6x O O O 6 0 1