If 5f(x) + 3f (1x) = x + 2 and y = x f(x), then (dydx)x=1 is equal to

Sail E0 Webinar

Question

If 5f(x) + 3f

(\frac{1}{x})

= x + 2 and y = x f(x), then

{(\frac{d y}{d x})}_{x = 1}

is equal to

Options:

A . 14

B . 78

C . 1

D . None of these

Answer: Option B
:
B

5 f (x) + 3 f (\frac{1}{x}) = x + 2 . . . . . . . . (i)

R e p l a c i n g x b y \frac{1}{x}

∴ 5 f (\frac{1}{x}) + 3 f (x) = \frac{1}{x} + 2 . . . (i i)

F r o m E q . (i) .

25 f (x) + 15 f (\frac{1}{x}) = 5 x + 10 . . . . (i i i)

a n d f r o m E q . (i i)

9 f (x) + 15 f (\frac{1}{x}) = \frac{3}{x} + 6 . . . . . (i v)

S u b t r a c t i n g E q . (i v) f r o m (i i i), w e g e t

∴ 16 f (x) = 5 x - \frac{3}{x} + 4

∴ x f (x) = \frac{5 x^{2} - 3 + 4 x}{16} = y

∴ \frac{d y}{d x} = \frac{10 x + 4}{16}

∴ \frac{d y}{d x} |_{x = 1} = \frac{10 + 4}{16}

= \frac{7}{8}

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If y=√sin x+√sin x+√sin x+.....∞,then dydx is equal ....If y=√sin x+√sin x+√sin x+.....∞,then dydx is equal to

Question 2. If y=(ax+bcx+d) , then 2dydx.d3ydx3 is equal to....

Question 3. If xy.yx=16,then dydx at (2,2) is....

Question 4. If f(x)=(logcotxtan x)(logtanxcot x)−1+tan−1(x√(4−x2)) then f'(0) is equ....If f(x)=(logcotxtan x)(logtanxcot x)−1+tan−1(x√(4−x2)) then f'(0) is equal to

Question 5. If y=ln(xa+bx)x,then x3d2ydx2 is equal to....

Question 6. If x2+y2=t−1t and x4+y4=t2+1t2,then x3ydydx equals....

Question 7. If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to....

Question 8. If f(x) = sin−1(sin x)+cos−1(sin x) and ϕ(x)=f(f(f(x))),then ϕ′....If f(x) = sin−1(sin x)+cos−1(sin x) and ϕ(x)=f(f(f(x))),then ϕ′(x) is equal to

Question 9. If x=ey+ey+ey+ey+⋯∞....

Question 10. If y = tan−1√(1+sinx1−sinx),π2<x<π, then dydx equals ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0