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 \(\frac{d^2y}{dx^2}\)
  • \(\frac{3}{2}\)
  • \(\frac{3}{4t}\)
  • \(\frac{3}{2t}\)
  • \(\frac{3}{5t}\)
If y = ae+ be+ c Where a, b, c are parameters, they y’ is equal to
  • ae – be
  • ae + be
  • -(ae + be)
  • None of the above
let f(2) = 4 then f”(2) = 4 then \(\lim_{x\to 2}\) \(\frac{xf(2)-2f(x)}{x-2}\) is given by
  • 2
  • -2
  • -4
  • 3
If f(x) = \(\sqrt{1+\cos ^2(x^2)}\), then the value of f’ (\(\frac{√π}{2}\)) is
  • \(\frac{√π}{6}\)
  • –\(\frac{√π}{6}\)
  • \(\frac{1}{√6}\)
  • \(\frac{π}{√6}\)
Let f(x)={\(_{1-\cos x, for x ≤ 0}^{\sin x, for x > 0}\) and g (x) = e. Then the value of (g o f)’ (0) is
  • 1
  • -1
  • 0
  • None of these
If y = tan(\(\frac{\sin x+\cos x}{cox-\sin x}\)) then \(\frac{dy}{dx}\) is equal to
  • \(\frac{1}{2}\)
  • \(\frac{π}{4}\)
  • 0
  • 1
\(\frac{d}{dx}\)(x\(\sqrt{a^2-x^2}+a^2 \sin ^{-1}(\frac{x}{a})\)) is equal to
  • \(\sqrt{a^2-x^2}\)
  • 2\(\sqrt{a^2-x^2}\)
  • \(\frac{1}{\sqrt{a^2-x^2}}\)
  • None of these
If f(x) = tan(\(\sqrt{\frac{1+\sin x}{1-\sin x}}\)), 0 ≤ x ≤ \(\frac{π}{2}\), then f'(\(\frac{π}{6}\)) is
  • –\(\frac{1}{4}\)
  • –\(\frac{1}{2}\)
  • \(\frac{1}{4}\)
  • \(\frac{1}{2}\)
If y = \(\sqrt{\sin x+y}\) then \(\frac{dy}{dx}\) is equal to
  • \(\frac{\cos x}{2y-1}\)
  • \(\frac{\cos x}{1-2y}\)
  • \(\frac{\sin x}{1-xy}\)
  • \(\frac{\sin x}{2y-1}\)
If x sin (a + y) = sin y, then \(\frac{dy}{dx}\) is equal to
  • \(\frac{\sin ^2(a+y)}{sin a}\)
  • \(\frac{sin a}{\sin ^2(a+y)}\)
  • \(\frac{\sin (a+y)}{sin a}\)
  • \(\frac{sin a}{\sin (a+y)}\)
Derivative of the function f (x) = log(Iog,x), x > 7 is
  • None of these
  • \(\frac{1}{x(\log 5)(\log 7)(\log 7-x)}\)
  • \(\frac{1}{x(\log 5)(\log 7)}\)
  • \(\frac{1}{x(\log x)}\)
If y = log x + log y, then \(\frac{dy}{dx}\) is equal to
  • \(\frac{y}{y-1}\)
  • \(\frac{y}{x}\)
  • None of these
  • \(\frac{\log _{10}e}{x}\)(\(\frac{y}{y-1}\))
If x= y, then \(\frac{dy}{dx}\) is equal to
  • –\(\frac{y}{x}\)
  • –\(\frac{x}{y}\)
  • 1 + log (\(\frac{x}{y}\) )
  • \(\frac{1+\log x}{1+\log y}\)
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