lf the parametric equation of a curve given by $x=e^{t}\cos t,\ y=e^{t}\sin t$, then the tangent to the curve at the point $t=\dfrac{\pi}{4}$ makes with axis of $x$ the angle.

Let the function $y=f(x)$ be given by $x=t^{5}-5t^{3}-20t+7$ and $y=4t^{3}-3t^{2}-18t+3$, where $t\epsilon \left ( -2, 2 \right )$. Then $f^{'}(x)$ at $t=1$ is ?

x=a(θ-sinθ), y=a(1-cosθ) হলে -

1. $\frac{dy}{dx} = \cot{\left ( \frac{θ}{2} \right )}$  
2. $\frac{dx}{dy} = \frac{1 - \cos{θ}}{\sin{θ}}$  
3. $θ = \frac{π}{2}$ হলে $\frac{dy}{dx} = 1$

নিচের কোনটি সঠিক? 

  $y = \sin^{- 1}{\left [ \frac{4 \sqrt{x}}{1 + 4 x} \right ]}$ হলে,   $\left ( \frac{dy}{dx} \right )_{\left ( \left ( 4 , 2 \right ) \right.}$ এর মান কত?

If for $x \in \left(0, \dfrac{1}{4}\right)$, the derivative $\tan^{-1} \left(\dfrac{6x\sqrt{x}}{1-9x^{3}}\right)$ is $\sqrt{x}.g(x)$, then $g(x)$ equals :