List of top Mathematics Questions on Derivatives asked in KEAM

If $ x={{\sin }^{-1}}(3t-4{{t}^{3}}) $ and $ y={{\cos }^{-1}}(\sqrt{1-{{t}^{2}}}), $ then $ \frac{dy}{dx} $ is equal to

The total revenue in rupees received from the sale of x units of a product is given by $ R(x)=13{{x}^{2}}+26x+15 $ . Then, the marginal revolution rupees, when $ x=15 $ is

If $ y={{\sin }^{2}}{{\cot }^{-1}}\sqrt{\frac{1+x}{1-x}}, $ then $ \frac{dy}{dx} $ is equal to

Let $ \alpha $ and $ \beta $ be the roots of $ a{{x}^{2}}+bx+c=0 $ . Then, $ \underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}} $ is equal to

The value of $\displaystyle \lim_{y \to \infty} \left[y \, sin \left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to

The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to

$\displaystyle \lim_{x \to 2} $ $\frac{x^{100}-2^{100}}{x^{77}-2^{77}}$ is equal to

$ \underset{x\to 2}{\mathop{\lim }}\,\frac{{{x}^{100}}-{{2}^{100}}}{{{x}^{77}}-{{2}^{77}}} $ is equal to

$ \displaystyle\lim_{x\rightarrow0} \frac{1}{3-2^{\frac{1}{x}}}$ is equal to

$\displaystyle \lim_{x \to 0} $ $\frac{\left(1+2x\right)^{10}-1}{x}$ is equal to