Tan-14x1-5x2-tan-12-3x3-2x-

tan ^ 1 #160; ( 4x / 1+5 x^ 2 #160; ) +tan ^ 1 #160; ( 2+3x / 3 2x #160; ) #160; ⇒tan ^ 1 #160; ( 5xd x / 1+5x· x #160; ) + ...

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Basic Inverse Trigonometric Functions

tan-14x1+5x2+...

Question

${tan}^{- 1} (\frac{4 x}{1 + 5 x^{2}}) + {tan}^{- 1} (\frac{2 + 3 x}{3 - 2 x})$ .

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Solution

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{tan}^{- 1} (\frac{4 x}{1 + 5 x^{2}}) + {tan}^{- 1} (\frac{2 + 3 x}{3 - 2 x})

y = {tan}^{- 1} (\frac{4 x}{1 + 5 x^{2}}) + {tan}^{- 1} (\frac{2 + 3 x}{3 - 2 x})

\frac{d y}{d x}

If $y = t a n^{- 1} (\frac{4 x}{1 + 5 x^{2}}) + t a n^{- 1} (\frac{2 + 3 x}{3 - 2 x})$ then $\frac{d y}{d x} a t x = \frac{1}{5} i s$

y = t a n^{- 1} (\frac{4 x}{1 + 5 x^{2}}) + t a n^{- 1} (\frac{2 + 3 x}{3 - 2 x})

\frac{d y}{d x}

x = \frac{1}{5}

y = {tan}^{- 1} (\frac{4 x}{1 + 5 x^{2}}) + {cot}^{- 1} (\frac{3 - 2 x}{2 + 3 x})

\frac{d y}{d x}

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