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Standard Formulae - 1

If (sinx)^y=x...

Question

If (sinx)^y=x+y find dy/dx

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sin (x y) + \frac{x}{y} = x^{2} - y

\frac{d y}{d x}

sin (x y) + \frac{y}{x} = x^{2} + y^{2}

\frac{d y}{d x}

.

sin (x y) + cos (x y) = 0

\frac{d y}{d x} =

Q. Assertion :If

e^{x y} + log (x y) + sin (x y) - 2 = 0

\frac{d y}{d x} = \frac{- y}{x}

\frac{d (x y)}{d x} = 0

\Rightarrow

\frac{d y}{d x} = \frac{- y}{x}

\frac{d y}{d x}

x

y

are connected by the relation given:

sin (x y) + \frac{x}{y} = x^{2} - y

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