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Theorems for Differentiability

If y=x sin x ...

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If y=x sin x square, then the value of dy/dx is

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y = | sin x |^{| x |}

, then the value of

\frac{d y}{d x}

x = \frac{π}{6}

.

y = {sin}^{- 1} (\frac{\sqrt{1 + x} + \sqrt{1 - x}}{2})

, then the value of

\frac{d y}{d x}

x = 0

x sin y = sin (y + a)

\frac{d y}{d x} = \frac{A}{1 + x^{2} - 2 x cos a}

then the value of

A

Q. If sin y = x sin (a + y) and

\frac{d y}{d x} = \frac{A}{1 + x^{2} - 2 x c o s a^{'}},

then the value of A is

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

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