Use logarithmic differentiation to evaluate f'(x).

Question

Question

f(x) = (x + 3)¹⁰ / (4x - 4)¹²

f'(x) = _______

math calculus

Answer 1

Answer #1

Answer 2

Answer #2

SOLUTION :

f(x) = (x+3)^10 / (4x - 4)^12

Take natural log both sides :

=> ln (f (x)) = 10 ln(x+3) - 12 ln(4x - 4)

Differentiating w.r.t x :

=> 1 / f(x) * f ‘ (x) = (10 / (x+3)) * (1) - (12 / (4x - 4)) * (4)

=> f’ (x) / f(x) = 10 / (x+3) - 48 / (4x - 4)

=> f’ (x) = (10(4x-4) - 48(x+3)) / ((x+3)(4x-4)) * (x+3)^10 / (4x - 4)^12

=> f’ (x) = (-8x -184) (x+3)^9 / (4x-4)^13

=> f’ (x) = -8(x + 23) (x+3)^9 / (4x -4)^13 (ANSWER)

answered by: Tulsiram Garg

Answer 3

Similar Homework Help Questions

Use logarithmic differentiation to determine the derivative

Let $$ f(x)=\frac{x^{4}(x-3)^{2}}{\left(x^{2}+6\right)^{7}} $$Use logarithmic differentiation to determine the derivative f'(x) = f'(3) =
need steps 14. Use logarithmic differentiation to find the derivative of f(x) = n(x) at =...

need steps 14. Use logarithmic differentiation to find the derivative of f(x) = n(x) at = e.
Question No: 4 Marks: 1 + 2 + (2 + 2) + 2 a) Use logarithmic...

Question No: 4 Marks: 1 + 2 + (2 + 2) + 2 a) Use logarithmic differentiation to find y: y = (2x + 1)*** dx b) Find 5 (vp + xl at c) If f'(x) = 3 + 4x and the curve f(x) passes through the point (1,8) i) Find f(x) ii) Find the local extreme (if any) of f(x) using second derivative test. d) Evaluate using integration by parts: [(x + 2)In x dx Page 4 of 5

a) b) 54-1+1 Use logarithmic differentiation to find the first derivative of y= (3x² +2) 13...

a) b) 54-1+1 Use logarithmic differentiation to find the first derivative of y= (3x² +2) 13 Evaluate the integration I, where I = dt 5t2 3 If f'(x) == Vx+ and the curve f(x) passes through the point (0,2) 2 2 i) Find f(x) 11) Find the local extreme (if any) of f(x) using second derivative test. d) Evaluate using integration by parts: 5 (0)do, where f(O)=(0+1) sin 30 Page 4 of 5
please answer both questions Use logarithmic differentiation to differentiate the following function. f(x) = e *...

please answer both questions Use logarithmic differentiation to differentiate the following function. f(x) = e * (5x - 6) f'(x)= Which of the following is the same as 2 In (8x)? (a) In 16+ Inx (c) In (16x) (b) 16 In x (d) In (64x2) List all expressions that are equivalent. (Type a, b, c, or d. Use a comma to separate answers as needed.)
Use logarithmic differentiation to find the derivative of the function. Your answer should be in terms...

Use logarithmic differentiation to find the derivative of the function. Your answer should be in terms of x only, not y. y=(cos(x))^x Use logarithmic differentiation to find the derivative of the function. Your answer should be in terms of x only, not y. y = (cos(x))*

4. Use logarithmic differentiation to compute the derivative of y=(x + 1)*. Your answer should give...

4. Use logarithmic differentiation to compute the derivative of y=(x + 1)*. Your answer should give as an erplicit function of x only.
[x²+1 6. Use logarithmic differentiation to find the derivative: y = 1x2-1

[x²+1 6. Use logarithmic differentiation to find the derivative: y = 1x2-1
Use logarithmic differentiation to find the derivative y = x6 cos(x) Cham, M, Aarl

Use logarithmic differentiation to find the derivative y = x6 cos(x) Cham, M, Aarl

D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 +...

D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.

​Use logarithmic differentiation to evaluate f'(x).