If d2x-dy2 dy-dx 3-d2y-dx2-K then the value of K is equal to

The correct option is D 0 Let y=f(x) So, d yd x=f'(x) d xd y=1f'(x) d ^2xd y^2= f”(x).d xd y(f'(x))^2= f”(x).1f'(x)(f'(x))^2 and ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

If d2x/dy2 ...

Question

If $\frac{d^{2} x}{d y^{2}} {(\frac{d y}{d x})}^{3} + \frac{d^{2} y}{d x^{2}} = K$ then the value of $K$ is equal to

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Solution

The correct option is D $0$
Let $y = f (x)$
So, $\frac{d y}{d x} = f^{'} (x)$

$\frac{d x}{d y} = \frac{1}{f^{'} (x)}$

$\frac{d^{2} x}{d y^{2}} = \frac{- f^{''} (x) . \frac{d x}{d y}}{(f^{'} (x))^{2}} = \frac{- f^{''} (x) . \frac{1}{f^{'} (x)}}{(f^{'} (x))^{2}}$
and
$\frac{d^{2} y}{d x^{2}} = f^{''} (x)$

So, $\frac{d^{2} x}{d y^{2}} (\frac{d y}{d x})^{3} + \frac{d^{2} y}{d x^{2}}$

$= \frac{- f^{''} (x)}{(f^{'} (x))^{3}} . (f^{'} (x))^{3} + f^{''} (x) = 0 = K$

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If d2xdy2(dydx)3+d2ydx2=K then the value of K is equal to

The correct option is D 0Let y=f(x)So, dydx=f′(x)dxdy=1f′(x)d2xdy2=−f′′(x).dxdy(f′(x))2=−f′′(x).1f′(x)(f′(x))2and d2ydx2=f′′(x)So, d2xdy2(dydx)3+d2ydx2=−f′′(x)(f′(x))3.(f′(x))3+f′′(x)=0=K

If $\frac{d^{2} x}{d y^{2}} {(\frac{d y}{d x})}^{3} + \frac{d^{2} y}{d x^{2}} = K$ then the value of $K$ is equal to