LA

If $x=a\left(\cos\theta+\log\tan\frac{\theta}{2}\right)$ and $y=\sin\theta$, then find $\frac{d^{2}y}{dx^{2}}$ at $\theta=\frac{\pi}{4}$.

LA

Find the differential of $x^{\cot x}+\frac{2x^{2}-3}{2x^{2}-x+2}$ with respect to x.

SA

If $x=e^{cos~3t}$ and $y=e^{sin~3t}$ , prove that $\frac{dy}{dx}=-\frac{y~log~x}{x~log~y}$

MCQ_SINGLE

The derivative of \(\tan^{-1}(x^{2})\) w.r.t. x is :

SA

Find $\frac{dy}{dx}$ , if $(cos~x)^{y}=(cos~y)^{x}.$

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