If x sin (a + y) = sin y, then \(\frac{dy}{dx}\) is equal to
  • \(\frac{sin^2(a+y)}{sin a}\)
  • \(\frac{sin a}{sin^2(a+y)}\)
  • \(\frac{sin(a+y)}{sin a}\)
  • \(\frac{sin a}{sin(a+y)}\)
If x \(\sqrt{1+y}+y\sqrt{1+x}\) = 0, then \(\frac{dy}{dx}\) =
  • \(\frac{x+1}{x}\)
  • \(\frac{1}{1+x}\)
  • \(\frac{-1}{(1+x)^2}\)
  • \(\frac{x}{1+x}\)
If y = x tan y, then \(\frac{dy}{dx}\) =
  • \(\frac{tan x}{x-x^2-y^2}\)
  • \(\frac{y}{x-x^2-y^2}\)
  • \(\frac{tan y}{y-x}\)
  • \(\frac{tan x}{x-y^2}\)
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
  • \(\frac{y*2}{x^2}\)
  • \(\frac{2y\sqrt{y^2-1}(x^2+x-1)}{(x^2+1)^2}\)
  • \(\frac{(x^2+x-1)}{y\sqrt{y^2-1}}\)
  • \(\frac{x^2-y^2}{x^2+y^2}\)
If f(x) = \(\sqrt{1+cos^2(x^2)}\), then the value of f’ (\(\frac{√π}{2}\)) is
  • \(\frac{√π}{6}\)
  • –\(\frac{√π}{6}\)
  • \(\frac{1}{√6}\)
  • \(\frac{π}{√6}\)
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
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 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(\(\frac{sinx+cosx}{cox-sinx}\)) then \(\frac{dy}{dx}\) is equal to
  • \(\frac{1}{2}\)
  • \(\frac{π}{4}\)
  • 0
  • 1
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
\(\frac{d}{dx}\)(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(\(\sqrt{\frac{1+sinx}{1-sinx}}\)), 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 = 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
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