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
Derivative of the function f (x) = log(Iog,x), x > 7 is
  • \(\frac{1}{x(log5)(log7)(log7-x)}\)
  • \(\frac{1}{x(log5)(log7)}\)
  • \(\frac{1}{x(logx)}\)
  • None of these
If y = log x + log y, then \(\frac{dy}{dx}\) is equal to
  • \(\frac{y}{y-1}\)
  • \(\frac{y}{x}\)
  • \(\frac{log_{10}e}{x}\)(\(\frac{y}{y-1}\))
  • None of these
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 x= y, then \(\frac{dy}{dx}\) is equal to
  • –\(\frac{y}{x}\)
  • –\(\frac{x}{y}\)
  • 1 + log (\(\frac{x}{y}\) )
  • \(\frac{1+logx}{1+logy}\)
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
If x= e then \(\frac{dy}{dx}\) is
  • \(\frac{1+x}{1+log x}\)
  • \(\frac{1-log x}{1+log y}\)
  • not defined
  • \(\frac{-y}{(1+log x)^2}\)
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
x. y= 16, then the value of \(\frac{dy}{dx}\) at (2, 2) is
  • -1
  • 0
  • None of these
  • -2
If y = e find \(\frac{dy}{dx}\) =
  • \(\frac{y^2}{1-y}\)
  • \(\frac{y^2}{y-1}\)
  • \(\frac{y}{y-1}\)
  • \(\frac{-y}{y-1}\)
If x = \(\frac{1-t^2}{1+t^2}\) and y = \(\frac{2t}{1+t^2}\) then \(\frac{dy}{dx}\) is equal to dx
  • –\(\frac{y}{x}\)
  • \(\frac{y}{x}\)
  • –\(\frac{x}{y}\)
  • \(\frac{x}{y}\)
If x = a cosθ, y = a sinθ. then \(\frac{dy}{dx}\) at θ = \(\frac{3π}{4}\) is
  • -1
  • 1
  • -a²
  • a²
If x = sin(3t – 4t³) and y = cos(\(\sqrt{1-t^2}\)) then \(\frac{dy}{dx}\) is equal to
  • \(\frac{1}{2}\)
  • \(\frac{2}{5}\)
  • \(\frac{3}{2}\)
  • \(\frac{1}{3}\)
If x = e sin t, y = e cos t, t is a parameter, then \(\frac{dy}{dx}\) at (1, 1) is equal to
  • –\(\frac{1}{2}\)
  • –\(\frac{1}{4}\)
  • 0
  • \(\frac{1}{2}\)
The derivative of sin(\(\frac{2x}{1+x^2}\)) with respect to cos(\(\frac{1-x^2}{1+x^2}\)) is
  • -1
  • 1
  • 2
  • 4
If x = t², y = t³, then \(\frac{d^2y}{dx^2}\)
  • \(\frac{3}{2}\)
  • \(\frac{3}{4t}\)
  • \(\frac{3}{2t}\)
  • \(\frac{3}{5t}\)
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