VSA

Differentiate $\left(\frac{5^{x}}{x^{5}}\right)$ with respect to x.

SA

If $y=\log(\sqrt{x}+\frac{1}{\sqrt{x}})^{2}$, then show that $x(x+1)^{2}y_{2}+(x+1)^{2}y_{1}=2$.

SA

Differentiate $y=\sqrt{\log\left\{\sin\left(\frac{x^{3}}{3}-1\right)\right\}}$ with respect to x.

VSA

If $ \sqrt{3}\,(x^2+y^2)=4xy$, then find \(\dfrac{dy}{dx}\) at $\left(\frac{1}{2},\,\frac{\sqrt{3}}{2}\right).$

SA

If $(\sin x)^{y}=y^{\cos x}$ then find $\frac{dy}{dx}$.

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