TG EAPCET 2025 (Online) 3rd May Evening Shift | Differentiation Question 4 | Mathematics

If $y=\sqrt{\log \left(x^2+1\right)+\sqrt{\log \left(x^2+1\right)+\sqrt{\log \left(x^2+1\right)+\ldots+\infty}}, \text {, } 100.00}$, $|x|<1$, then $\frac{d y}{d x}=$

$\frac{x^2+1}{2 y-1}$

$\frac{2 x}{2 y-1}$

$\frac{1}{\left(x^2+1\right)(2 y-1)}$

$\frac{2 x}{\left(x^2+1\right)(2 y-1)}$

TG EAPCET 2025 (Online) 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

If $x=\sqrt{1-\tan y}$, then $\frac{d y}{d x}=$

$\frac{2 x}{x^4+2 x^2+2}$

$-\frac{2 x}{x^4-2 x^2+2}$

$\frac{2 x}{x^4-2 x^2+2}$

$-\frac{2 x}{x^4+2 x^2+2}$

TG EAPCET 2025 (Online) 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

If $x=\sin 2 \theta \cos 3 \theta, y=\sin 3 \theta \cos 2 \theta$, then $\frac{d y}{d x}=$

$\frac{2 \cos 5 \theta+\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$

$\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}$

$\frac{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}$

$\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$

TG EAPCET 2025 (Online) 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

If $3^x y^x=x^{3 y}$, then the value of $\frac{d y}{d x}$ at $x=1$ is

-3

$-\frac{1}{3}$

$\frac{1}{3}$

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