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Derivative of One Function w.r.t Another

If y⁴+5xy+y=2...

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If y⁴+5xy+y=2 then find the value of dy/dx and d²y/dx².

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y = e^{a x} cos b x

, then find the value of

\frac{d^{2} y}{d x^{2}} - 2 a \frac{d y}{d x} + (a^{2} + b^{2}) y

.

d x + d y = (x + y) (d x - d y)

then fine the value of log(x+y).

x + y = t a n^{- 1} y a n d \frac{d^{2} y}{d x^{2}} = f (y) \frac{d y}{d x}

f (y) =

y = a cos (log x) - b sin (log x)

, then the value of

x^{2} \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + y

y = {sin}^{- 1} (2 x)

\frac{d y}{d x}

y = x^{2 x}

\frac{d y}{d x}

.

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