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If y=a sin x + b cos x, then ((dy)/dx)^...

If ` y=a sin x + b cos x`, then `((dy)/dx)^2+y^2` is

A

function of x

B

function of y

C

function of x and y

D

constant

Text Solution

AI Generated Solution

To solve the problem, we need to find the expression \(\left(\frac{dy}{dx}\right)^2 + y^2\) given that \(y = a \sin x + b \cos x\). ### Step-by-Step Solution: 1. **Differentiate \(y\) with respect to \(x\)**: \[ y = a \sin x + b \cos x \] ...
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Knowledge Check

  • If y = (cos x - sin x)/( cos x + sin x ) , "then " (dy)/(dx)

    A
    `x^(2)`
    B
    `y^(2)`
    C
    `1 + y^(2)`
    D
    `- (1 + y^(2))`

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