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If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)...

If `e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((1-t)/(1+t))` ,then `(dy)/(dx)` at `t=1/2` is (a)`-1/2` (b) `1/2` (c) 0 (d) none of these

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

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  2. If e^y(x+1)=1, show that (d^2y)/(dx^2)=((dy)/(dx))^2

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  3. If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((...

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  4. If y=cos^(-1)(cosx),then (dy)/(dx) at x=(5pi)/4 is equal to (a)1 (b)-...

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  5. If y=cos^(-1)(cosx),t h e n(dy)/(dx) at x=(5pi)/4 is equal to (a) 1 (b...

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  6. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to (a...

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  7. If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt...

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  8. If y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2), then (dy)/...

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  9. The derivative of y=(1-x)(2-x)....(n-x) at x=1 is (a)0 (b) (-1)(...

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  10. If y=sqrt((1-x)/(1+x)), prove that ((1-x^2)dy)/(dx)+y=0

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  11. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

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  12. Differentiate x^2+\ 1 with respect to x .

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  13. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

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  14. Given y= Sin 2x + x^3 , (dy)/(dx)

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  15. Find the derivative of f(x)=e^(4x) + Cos 3x

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  16. A nonzero polynomial with real coefficient has the property that f(x)=...

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  17. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f''(x)-2f^(prime)...

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  18. Let z=(cosx)^5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=(...

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  19. A function is reprersented parametrically by the equations x=(1+t)/(t^...

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  20. Let f be a twice differentiable function such that f^(prime prime)(x)=...

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