AP EAPCET 2024 - 18th May Morning Shift | Differentiation Question 19 | Mathematics

If $x=3\left[\sin t-\log \left(\cot \frac{t}{2}\right)\right]$ and $y=6\left[\cos t+\log \left(\operatorname{tin} \frac{t}{2}\right)\right]$ then $\frac{d y}{d x}=$

$\frac{2 \sin ^2 t}{1+\sin t \cos t}$

$\frac{2 \cos ^2 t}{1+\sin 2 t}$

$\frac{2 \cos ^2 t}{1+\sin t \cos t}$

$\frac{1+\cos g}{1+\sin a}$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

-0

The length of the tangent drawn at the point $P\left(\frac{\pi}{4}\right)$ on the curve $x^{2 / 3}+y^{2 / 3}=2^{2 / 3}$ is

$\frac{2}{3}$

$\frac{4}{3}$

AP EAPCET 2022 - 5th July Morning Shift

MCQ (Single Correct Answer)

-0

Assertion (A) $$\frac{d}{d x}\left(\frac{x^2 \sin x}{\log x}\right)=\frac{x^2 \sin x}{\log x}\left(\cot x+\frac{2}{x}-\frac{1}{x \log x}\right)$$

Reason (R) $$\frac{d}{d x}\left(\frac{u v}{w}\right)=\frac{u v}{w}\left[\frac{u^{\prime}}{u}+\frac{v^{\prime}}{v}+\frac{w^{\prime}}{w}\right]$$

A is true, R is true and R is correct explanation of A

A is true, R is true and R is not correct explanation of A

A is true, R is not correct

A is not correct, R is correct

AP EAPCET 2022 - 5th July Morning Shift

MCQ (Single Correct Answer)

-0

If $$x=f(\theta)$$ and $$y=g(\theta)$$, then $$\frac{d^2 y}{d x^2}=$$

$$\frac{g^{\prime \prime}(\theta)}{f^{\prime}(\theta)}$$

$$\frac{f^{\prime \prime}(\theta)}{x(\theta)}$$

$$\frac{f^{\prime}(\theta) g^{\prime \prime}(\theta)-g^{\prime}(\theta) f^{\prime \prime}(\theta)}{\left(f^{\prime}(\theta)\right)^3}$$

$$\frac{g^{\prime}(\theta) f^{\prime \prime}(\theta)-g^{\prime \prime}(\theta) f^{\prime \prime}(\theta)}{\left(g^{\prime \prime}(\theta)\right)^3}$$

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