# Differentiation · Mathematics · AP EAPCET

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AP EAPCET 2022 - 4th July Morning Shift
If $$f(x)=\cot ^{-1}\left(\frac{x^x+x^{-x}}{2}\right)$$, then $$f^{\prime}(1)=$$
AP EAPCET 2021 - 20th August Morning Shift
If $$f(x)=2x^2+3x-5$$, then the value of $$f'(0)+3f'(-1)$$ is equal to
AP EAPCET 2021 - 20th August Morning Shift
If $$y=\left(1+\frac{1}{x}\right)\left(1+\frac{2}{x}\right)\left(1+\frac{3}{x}\right) \ldots\left(1+\frac{n}{x}\right)$$ and $$x \neq 0$$. When $$x=-1... AP EAPCET 2021 - 19th August Evening Shift If$$\log \left(\sqrt{1+x^2}-x\right)=y\left(\sqrt{1+x^2}\right)$$, then$$\left(1+x^2\right) \frac{d y}{d x}+x y$$is equal to AP EAPCET 2021 - 19th August Evening Shift If$$y=e^{x^2+e^{x^2+e^{x^2+\cdots \infty}}}$$, then$$\frac{d y}{d x}$$is equal to AP EAPCET 2021 - 19th August Evening Shift$$\frac{d}{d x}\left[\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right)\right]$$is equal to AP EAPCET 2021 - 19th August Evening Shift If$$x^2+y^2=1$$, then AP EAPCET 2021 - 19th August Morning Shift If$$y=x+\frac{1}{x}$$, then which among the following holds? AP EAPCET 2021 - 19th August Morning Shift If$$3 \sin x y+4 \cos x y=5$$, then$$\frac{d y}{d x}$$is equal to AP EAPCET 2021 - 19th August Morning Shift$$f(x)=\sqrt{x^2+1}: g(x)=\frac{x+1}{x^2+1}: h(x)=2 x-3$$, then the value of$$f^{\prime}\left[h^{\prime}\left(g^{\prime}(x)\right)\right]$$is equal ... AP EAPCET 2021 - 19th August Morning Shift For which value(s) of$$af(x)=-x^3+4 a x^2+2 x-5$$is decreasing for every$$x ?
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