Home
Class 12
MATHS
If y=asinx+bcosx ,t h e ny^2+((dy)/(dx))...

If `y=asinx+bcosx ,t h e ny^2+((dy)/(dx))^2` is a function of `x` (b) function of`y` function of `xa n dy` (d) constant

A

function of x

B

function of y

C

function of x and y

D

constant

Text Solution

Verified by Experts

y=a sin x + b cos x
Differentiating with respect to x, we get
`(dy)/(dx)=a cos x - b sin x`
`"Now, "((dy)/(dx))^(2)=(a cos x - b sin x)^(2)`
`=a^(2)cos^(2)x+b^(2)sin^(2)x-2ab sin x cos x`
`"and "y^(2)=(a sin x + b cos x)^(2)`
`a^(2)sin^(2) x +b^(2)cos^(2) x +2ab sin x cos x`
`"So, "((dy)/(dx))^(2)+y^(2)=a^(2)(sin^(2)x + cos^(2)x)+b^(2)(sin^(2)x+ cos^(2)x)`
`=(a^(2)+b^(2))=` constant
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|23 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If y=asinx+bcosx , then y^2+((dy)/(dx))^2 is a (a)function of x (b) function of y (c)function of x and y (d) constant

If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a function of x only (c) a function of y only (d) a function of x and y

Knowledge Check

  • If y=sinx+e^(x) , then the value of (d^(2)x)/(dy^(2)) is -

    A
    `(sinx-e^(x))/((cosx+e^(x))^(3))`
    B
    `(1)/(e^(x)-sinx)`
    C
    `(sinx-e^(x))/((cosx +e^(x))^(2))`
    D
    `(sinx+e^(x))/((cosx+e^(x))^(3))`

    • Similar Questions

    Explore conceptually related problems

    If x=t^(2) and y=log t , find (dy)/(dx) .

    Find (dy)/(dx) for the function: y= Sin 5x

    Find (dy)/(dx) for the function: y= x^(1/2) + Sin 2x

    Solve : (dy)/(dx)=e^(y-x)+2

    Find (dy)/(dx) for the function: y=e^x + cos x

    If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx) at x=0 is

    Find (dy)/(dx) for the function: y= sin x + ln x

    Home
    Profile