If fx- 2x x 2 x 3 x 2 -2x 1 3x-1 2x 1-3 x 2 5x - then find f-1

Que. f(x)=| 2x amp; x ^ 2 amp; x ^ 3 x ^ 2 +2x amp; 1 amp; 3x+1 2x amp; 1 3 x ^ 2 amp; 5x | , then #160; f'(1) ...

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Determinant

If fx=| 2x ...

Question

If $f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 x & x^{2} & x^{3} x^{2} + 2 x & 1 & 3 x + 1 2 x & 1 - 3 x^{2} & 5 x \end{matrix} ∣ ∣ ∣ ∣ ∣$ , then find $f^{'} (1)$

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Solution

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f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 x & x^{2} & x^{3} x^{2} + 2 x & 1 & 3 x + 1 2 x & 1 - 3 x^{2} & 5 x \end{matrix} ∣ ∣ ∣ ∣ ∣

f^{^{'}} (1)

f (x) = {sin}^{- 1} (\frac{2 x}{1 + x^{2}}),

f (x)

u = \sin^{- 1} (\frac{2 x}{1 + x^{2}}) and v = \tan^{- 1} (\frac{2 x}{1 - x^{2}})

- 1 < x < 1

\frac{d u}{d v}

f (x) = 1 + x + x^{2} + . . . . . + x^{100}

f^{'} (1)

y = \{\log_{\cos x} \sin x\} {\{\log_{\sin x} \cos x\}}^{- 1} + \sin^{- 1} (\frac{2 x}{1 + x^{2}}), find \frac{d y}{d x} a t x = \frac{π}{4}

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