If x y = e x − y then d y d x = Options: A . &nbsp(1+ln x)−1 B . &nbsp(1+ln x)−2 C . &nbspln x(1+ln x)−2 D . &nbspNone of these

Answer: Option C : C S i n c e , x y = e x − y ⇒ y ln x = x − y ∴ y = x 1 + ln x ∴ d y d x = ln x ( 1 + ln x ) 2

If xy=ex−y then dydx=

Question

x^{y} = e^{x - y}

then

\frac{d y}{d x} =

Options:

A . (1+ln x)−1

B . (1+ln x)−2

C . ln x(1+ln x)−2

D . None of these

Answer: Option C
:
C

S i n c e, x^{y} = e^{x - y} \Rightarrow y ln x = x - y ∴ y = \frac{x}{1 + ln x} ∴ \frac{d y}{d x} = \frac{ln x}{(1 + ln x)^{2}}

Was this answer helpful ?

Next Question

Question 1. If y=√(1+cos 2 θ1−cos2 θ),dydθ at θ=3π4 i....If y=√(1+cos 2 θ1−cos2 θ),dydθ at θ=3π4 is

Question 2. If x=secθ−cosθ,y=sec10θ−cos10θ and (x2+4)(dydx)2=k(y2+4), then k is equal to....

Question 3. If sin y = x sin (a + y) and dydx=A1+x2−2xcos a′, then the value of A is....

Question 4. The derivative of cos−1(x−1−xx−1+x) at x=−1 is....

Question 5. If f(x) = |x|, then f’(x), where x ≠ 0 is equal to....

Question 6. If xcos y+ycos x=5. Then....

Question 7. If sin (x+y)=loge(x+y),thendydx is equal to....

Question 8. If x = a cos θ,y=b sin θ,then d3ydx3 is equal to....

Question 9. If √(1−x2n)+√(1−y2n)=a(xn−yn), then √(1−x2n1−y2n)dydx is equal t....If √(1−x2n)+√(1−y2n)=a(xn−yn), then √(1−x2n1−y2n)dydx is equal to

Question 10. If y=√x+√y+√x+√y+....∞, then dydx is equal to....

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

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0