Differentiation of Function
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Limits, Continuity and Differentiability

80268 If \(y=\sin \left[2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-\mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{-x}{1+x^{2}}\)
3 \(\frac{\mathrm{x}}{1+\mathrm{x}^{2}}\)
4 \(\frac{x}{\sqrt{1-x^{2}}}\)
MHT CET-2019
Limits, Continuity and Differentiability

80269 If \(y=\log (\sec \theta+\tan \theta)\) and \(x=\sec \theta\), then \(\frac{d y}{d x}\) at \(\theta=\frac{\pi}{4}\) is

1 \(\frac{1}{2}\)
2 2
3 -1
4 1
MHT CET-2019
Limits, Continuity and Differentiability

80270 If \(\log _{10}\left(\frac{x^{3}-y^{3}}{x^{3}+y^{3}}\right)=2\) and \(\frac{d y}{d x}=k \frac{x^{2}}{y^{2}}\) then \(k=\)

1 \(\frac{99}{101}\)
2 \(\frac{-101}{99}\)
3 \(\frac{-99}{101}\)
4 \(\frac{101}{99}\)
MHT CET-2016
Limits, Continuity and Differentiability

80271 If \(y=\tan ^{-1}\left[\frac{\log (e x)}{\log \left(\frac{e}{x}\right)}\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{1+(\log x)^{2}}\)
2 \(\frac{x}{1+(\log x)^{2}}\)
3 \(\frac{1}{x\left[1+(\log x)^{2}\right]}\)
4 \(\frac{-1}{x\left[1+(\log x)^{2}\right]}\)
MHT CET-2019
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

80268 If \(y=\sin \left[2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-\mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{-x}{1+x^{2}}\)
3 \(\frac{\mathrm{x}}{1+\mathrm{x}^{2}}\)
4 \(\frac{x}{\sqrt{1-x^{2}}}\)
MHT CET-2019
Limits, Continuity and Differentiability

80269 If \(y=\log (\sec \theta+\tan \theta)\) and \(x=\sec \theta\), then \(\frac{d y}{d x}\) at \(\theta=\frac{\pi}{4}\) is

1 \(\frac{1}{2}\)
2 2
3 -1
4 1
MHT CET-2019
Limits, Continuity and Differentiability

80270 If \(\log _{10}\left(\frac{x^{3}-y^{3}}{x^{3}+y^{3}}\right)=2\) and \(\frac{d y}{d x}=k \frac{x^{2}}{y^{2}}\) then \(k=\)

1 \(\frac{99}{101}\)
2 \(\frac{-101}{99}\)
3 \(\frac{-99}{101}\)
4 \(\frac{101}{99}\)
MHT CET-2016
Limits, Continuity and Differentiability

80271 If \(y=\tan ^{-1}\left[\frac{\log (e x)}{\log \left(\frac{e}{x}\right)}\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{1+(\log x)^{2}}\)
2 \(\frac{x}{1+(\log x)^{2}}\)
3 \(\frac{1}{x\left[1+(\log x)^{2}\right]}\)
4 \(\frac{-1}{x\left[1+(\log x)^{2}\right]}\)
MHT CET-2019
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Limits, Continuity and Differentiability

80268 If \(y=\sin \left[2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-\mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{-x}{1+x^{2}}\)
3 \(\frac{\mathrm{x}}{1+\mathrm{x}^{2}}\)
4 \(\frac{x}{\sqrt{1-x^{2}}}\)
MHT CET-2019
Limits, Continuity and Differentiability

80269 If \(y=\log (\sec \theta+\tan \theta)\) and \(x=\sec \theta\), then \(\frac{d y}{d x}\) at \(\theta=\frac{\pi}{4}\) is

1 \(\frac{1}{2}\)
2 2
3 -1
4 1
MHT CET-2019
Limits, Continuity and Differentiability

80270 If \(\log _{10}\left(\frac{x^{3}-y^{3}}{x^{3}+y^{3}}\right)=2\) and \(\frac{d y}{d x}=k \frac{x^{2}}{y^{2}}\) then \(k=\)

1 \(\frac{99}{101}\)
2 \(\frac{-101}{99}\)
3 \(\frac{-99}{101}\)
4 \(\frac{101}{99}\)
MHT CET-2016
Limits, Continuity and Differentiability

80271 If \(y=\tan ^{-1}\left[\frac{\log (e x)}{\log \left(\frac{e}{x}\right)}\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{1+(\log x)^{2}}\)
2 \(\frac{x}{1+(\log x)^{2}}\)
3 \(\frac{1}{x\left[1+(\log x)^{2}\right]}\)
4 \(\frac{-1}{x\left[1+(\log x)^{2}\right]}\)
MHT CET-2019
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Limits, Continuity and Differentiability

80268 If \(y=\sin \left[2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-\mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{-x}{1+x^{2}}\)
3 \(\frac{\mathrm{x}}{1+\mathrm{x}^{2}}\)
4 \(\frac{x}{\sqrt{1-x^{2}}}\)
MHT CET-2019
Limits, Continuity and Differentiability

80269 If \(y=\log (\sec \theta+\tan \theta)\) and \(x=\sec \theta\), then \(\frac{d y}{d x}\) at \(\theta=\frac{\pi}{4}\) is

1 \(\frac{1}{2}\)
2 2
3 -1
4 1
MHT CET-2019
Limits, Continuity and Differentiability

80270 If \(\log _{10}\left(\frac{x^{3}-y^{3}}{x^{3}+y^{3}}\right)=2\) and \(\frac{d y}{d x}=k \frac{x^{2}}{y^{2}}\) then \(k=\)

1 \(\frac{99}{101}\)
2 \(\frac{-101}{99}\)
3 \(\frac{-99}{101}\)
4 \(\frac{101}{99}\)
MHT CET-2016
Limits, Continuity and Differentiability

80271 If \(y=\tan ^{-1}\left[\frac{\log (e x)}{\log \left(\frac{e}{x}\right)}\right]\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{1+(\log x)^{2}}\)
2 \(\frac{x}{1+(\log x)^{2}}\)
3 \(\frac{1}{x\left[1+(\log x)^{2}\right]}\)
4 \(\frac{-1}{x\left[1+(\log x)^{2}\right]}\)
MHT CET-2019