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If u and v are two differentiable functi...

If u and v are two differentiable functions of x show that,
`(d)/(dx)("tan"^(-1)(u)/(v))=(v (du)/(dx)-u(dv)/(dx))/(u^(2)+v^(2))`.

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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A (Very Short Answer Type Questions)
  1. In each of the following cases find (dy)/(dx) using the rule (dy)/(dx...

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  2. In each of the following cases find (dy)/(dx) using the rule (dy)/(dx...

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  3. If u and v are two differentiable functions of x show that, (d)/(dx)...

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  4. Using the formula (d)/(dx)(tan^(-1)x)=(1)/(1+x^(2)), deduce that (d)/...

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  5. Find the derivatives w.r.t. x : 2 "tan"^(-1)(x)/(a)

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  6. Find the derivatives w.r.t. x : log (cot^(-1)x)

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  7. Find the derivatives w.r.t. x : sec(tan^(-1)x)

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  8. Find the derivatives w.r.t. x : 2 sec^(-1) 2x-3 sin^(-1)x+cos^(-1)(...

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  9. Find the derivatives w.r.t. x : 2"cosec"^(-1)(3x)+3"cosec"2x

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  10. Find the derivatives w.r.t. x : cos^(-1)x+cos^(-1)sqrt(1-x^(2))

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  11. Find the derivatives w.r.t. x : {f(x)}^(n)

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  12. Find the derivatives w.r.t. x : e^(phi(x))

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  13. Find the derivatives w.r.t. x : log[sqrt(f(x))]

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  14. Find the derivatives w.r.t. x : 3^(u(x))

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  15. Find the derivatives w.r.t. x : sin{f(x)}

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  16. Find the derivatives w.r.t. x : sec phi(x)

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  17. Find the derivatives w.r.t. x : cos^(-1)[f(x)]

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  18. Find the derivatives w.r.t. x : tan^(-1)[phi (x)]

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  19. Find the derivatives w.r.t. x : (2x^(2)+3)^(4)

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  20. Find the derivatives w.r.t. x : sqrt(x^(2)+a^(2))

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