If y = (1 + x) (1 + x²) (1 + x) …….. (1 + x), then the value of \(\frac{dy}{dx}\) at x = 0 is
  • 0
  • -1
  • 1
  • None of these
If f(x) = \(\frac{5x}{(1-x)^{2/3}}\) + cos² (2x + 1), then f'(0) =
  • 5 + 2 sin 2
  • 5 + 2 cos 2
  • 5 – 2 sin 2
  • 5 – 2 cos 2
If sec(\(\frac{x^2-2x}{x^2+1}\)) – y then \(\frac{dy}{dx}\) is equal to
  • \(\frac{y*2}{x^2}\)
  • \(\frac{2y\sqrt{y^2-1}(x^2+x-1)}{(x^2+1)^2}\)
  • \(\frac{(x^2+x-1)}{y\sqrt{y^2-1}}\)
  • \(\frac{x^2-y^2}{x^2+y^2}\)
Differential coefficient of \(\sqrt{sec√x}\) is
  • \(\frac{1}{4√x}\) = sec √x sin √x
  • \(\frac{1}{4√x}\) = (sec√x)sin√x
  • \(\frac{1}{2}\) √x sec√x sin √x. (d) \(\frac{1}{2}\)√x (sec√x)sin√x
If x y= (x + y), then \(\frac{dy}{dx}\) is equal to
  • \(\frac{x+y}{xy}\)
  • xy
  • \(\frac{x}{y}\)
  • \(\frac{y}{x}\)
If ax² + 2hxy + by² = 1, then \(\frac{dy}{dx}\)equals
  • \(\frac{hx+by}{ax+by}\)
  • \(\frac{ax+by}{hx+by}\)
  • \(\frac{ax+hy}{hx+hy}\)
  • \(\frac{-(ax+hy)}{hx+by}\)
If sec (\(\frac{x-y}{x+y}\)) = a then \(\frac{dy}{dx}\) is
  • –\(\frac{y}{x}\)
  • \(\frac{x}{y}\)
  • –\(\frac{x}{y}\)
  • \(\frac{y}{x}\)
If y = tan(\(\frac{√x-x}{1+x^{3/2}}\)), then y'(1) is equal to
  • 0
  • (\(\frac{√x-x}{1+x^{3/2}}\))
  • -1
  • –\(\frac{1}{4}\)
The differential coefficient of tan(\(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\)) is
  • \(\sqrt{1-x^2}\)
  • \(\frac{1}{\sqrt{1-x^2}}\)
  • \(\frac{1}{2\sqrt{1-x^2}}\)
  • x
If y = sin(\(\frac{√x-1}{√x+1}\)) + sec(\(\frac{√x+1}{√x-1}\)), x > 0, then \(\frac{dy}{dx}\) is equal to
  • 1
  • 0
  • \(\frac{π}{2}\)
  • None of these
If x = exp {tan(\(\frac{y-x^2}{x^2}\))}, then \(\frac{dy}{dx}\) equals
  • 2x [1 + tan (log x)] + x sec² (log x)
  • x [1 + tan (log x)] + sec² (log x)
  • 2x [1 + tan (logx)] + x² sec² (log x)
  • 2x [1 + tan (log x)] + sec² (log x)
If y = e, then the value of \(\frac{dy}{dx}\)|is
  • 1
  • 0
  • -1
  • 3e
Let f (x) = e, g (x) = sin x and h (x) = f |g(x)|, then \(\frac{h'(x)}{h(x)}\) is equal to
  • e
  • \(\frac{1}{\sqrt{1-x^2}}\)
  • sin x
  • \(\frac{1}{(1-x^2)}\)
If sin y + e= e, then \(\frac{dy}{dx}\) at (1, π) is equal to
  • sin y
  • -x cos y
  • e
  • sin y – x cos y
If y = log [e(\(\frac{x-1}{x-2}\))\(^{1/2}\)], then \(\frac{dy}{dx}\) is equal to
  • 7
  • \(\frac{3}{x-2}\)
  • \(\frac{3}{(x-1)}\)
  • None of these
If y = e, then \(\frac{dy}{dx}\) is equal to
  • \(\frac{1}{2}\) sec² x
  • sec² x
  • sec x tan x
  • e
If y = 23 then \(\frac{dy}{dx}\) is equal to dx
  • (log 2) (log 3)
  • (log lg)
  • (log 18²) y²
  • y (log 18)
If y = (tan x), then \(\frac{dy}{dx}\) is equal to
  • sec x + cos x
  • sec x+ log tan x
  • (tan x)
  • None of these
The derivative of y = (1 – x) (2 – x)…. (n – x) at x = 1 is equal to
  • 0
  • (-1) (n – 1)!
  • n ! – 1
  • (-1)
If f(x) = cos x, cos 2 x, cos 4 x, cos 8 x, cos 16 x, then the value of'(\(\frac{π}{4}\)) is
  • 1
  • √2
  • \(\frac{1}{√2}\)
  • 0
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