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  • Can someone explain - Limit , continuity and differentiability - JEE Main-7

If x^{2}+y^{2}+\sin y=4,  then the value of \frac{d^{2}y}{dx^{2}} at the point (-2,0) is : 

  • Option 1)

    -34

  • Option 2)

    -32

  • Option 3)

    4

  • Option 4)

    -2

 

Answers (2)

best_answer

As we learned

 

Derivative at a point -

The value of  f'(x) obtained by putting  x = a is called the derivative of  f(x) at  x = a  and it is denoted by  f'(a)  or  

\frac{dy}{dx}     at  x = a.

-

 

 

x^{2}+y^{2}+\sin y=4

On Differentiating , we get 

\frac{\mathrm{dy} }{\mathrm{d} x}=-\left ( \frac{2x}{2y+\cos y} \right )

at (-2,0) 

\frac{\mathrm{dy} }{\mathrm{d} x}=4

\frac{\mathrm{d^{2}y} }{\mathrm{d} x^{2}}=-\left [ \frac{\left ( 2y+\cos y \right )\left ( 2x \right )}{\left ( 2y+\cos y \right )^{2}}-\left ( 2y+\cos y \right ){}'\left ( 2x \right ) \right ]

at (-2,0) 

\frac{\mathrm{d^{2}y} }{\mathrm{d} x^{2}}=-34


Option 1)

-34

Option 2)

-32

Option 3)

4

Option 4)

-2

Posted by

Himanshu

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