Differentiation of Function
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Limits, Continuity and Differentiability

80315 If \(x=2 a t^{2}\) and \(y=a t^{4}\), then \(\frac{d^{2} y}{d x^{2}}\) at \(t=2\) is

1 4
2 \(2 \mathrm{a}\)
3 \(\frac{1}{2 \mathrm{a}}\)
4 \(-\frac{1}{2 \mathrm{a}}\)
MHT CET-2013
Limits, Continuity and Differentiability

80316 If \(y=\tan ^{-1}\left(\frac{4 x}{1+5 x^{2}}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)\), then \(\frac{d y}{d x}\)
is

1 \(\frac{-5}{1+25 \mathrm{x}^{2}}\)
2 \(\frac{5}{1+25 \mathrm{x}^{2}}\)
3 \(\frac{5}{1-25 \mathrm{x}^{2}}\)
4 0
MHT CET-2013
Limits, Continuity and Differentiability

80317 Derivative of \(\tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right)\) with respect to \(\sin ^{-1}\left(3 x-4 x^{3}\right)\) is

1 \(\frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{3}{\sqrt{1-\mathrm{x}^{2}}}\)
3 3
4 \(\frac{1}{3}\)
MHT CET-2016
Limits, Continuity and Differentiability

80318 Derivative of \(\log (\sec \theta+\tan \theta)\) with respect to
\(\sec \theta\) at \(\theta=\frac{\pi}{4}\) is

1 0
2 1
3 \(\frac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
MHT CET-2016
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Limits, Continuity and Differentiability

80315 If \(x=2 a t^{2}\) and \(y=a t^{4}\), then \(\frac{d^{2} y}{d x^{2}}\) at \(t=2\) is

1 4
2 \(2 \mathrm{a}\)
3 \(\frac{1}{2 \mathrm{a}}\)
4 \(-\frac{1}{2 \mathrm{a}}\)
MHT CET-2013
Limits, Continuity and Differentiability

80316 If \(y=\tan ^{-1}\left(\frac{4 x}{1+5 x^{2}}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)\), then \(\frac{d y}{d x}\)
is

1 \(\frac{-5}{1+25 \mathrm{x}^{2}}\)
2 \(\frac{5}{1+25 \mathrm{x}^{2}}\)
3 \(\frac{5}{1-25 \mathrm{x}^{2}}\)
4 0
MHT CET-2013
Limits, Continuity and Differentiability

80317 Derivative of \(\tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right)\) with respect to \(\sin ^{-1}\left(3 x-4 x^{3}\right)\) is

1 \(\frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{3}{\sqrt{1-\mathrm{x}^{2}}}\)
3 3
4 \(\frac{1}{3}\)
MHT CET-2016
Limits, Continuity and Differentiability

80318 Derivative of \(\log (\sec \theta+\tan \theta)\) with respect to
\(\sec \theta\) at \(\theta=\frac{\pi}{4}\) is

1 0
2 1
3 \(\frac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
MHT CET-2016
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

80315 If \(x=2 a t^{2}\) and \(y=a t^{4}\), then \(\frac{d^{2} y}{d x^{2}}\) at \(t=2\) is

1 4
2 \(2 \mathrm{a}\)
3 \(\frac{1}{2 \mathrm{a}}\)
4 \(-\frac{1}{2 \mathrm{a}}\)
MHT CET-2013
Limits, Continuity and Differentiability

80316 If \(y=\tan ^{-1}\left(\frac{4 x}{1+5 x^{2}}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)\), then \(\frac{d y}{d x}\)
is

1 \(\frac{-5}{1+25 \mathrm{x}^{2}}\)
2 \(\frac{5}{1+25 \mathrm{x}^{2}}\)
3 \(\frac{5}{1-25 \mathrm{x}^{2}}\)
4 0
MHT CET-2013
Limits, Continuity and Differentiability

80317 Derivative of \(\tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right)\) with respect to \(\sin ^{-1}\left(3 x-4 x^{3}\right)\) is

1 \(\frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{3}{\sqrt{1-\mathrm{x}^{2}}}\)
3 3
4 \(\frac{1}{3}\)
MHT CET-2016
Limits, Continuity and Differentiability

80318 Derivative of \(\log (\sec \theta+\tan \theta)\) with respect to
\(\sec \theta\) at \(\theta=\frac{\pi}{4}\) is

1 0
2 1
3 \(\frac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
MHT CET-2016
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Limits, Continuity and Differentiability

80315 If \(x=2 a t^{2}\) and \(y=a t^{4}\), then \(\frac{d^{2} y}{d x^{2}}\) at \(t=2\) is

1 4
2 \(2 \mathrm{a}\)
3 \(\frac{1}{2 \mathrm{a}}\)
4 \(-\frac{1}{2 \mathrm{a}}\)
MHT CET-2013
Limits, Continuity and Differentiability

80316 If \(y=\tan ^{-1}\left(\frac{4 x}{1+5 x^{2}}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)\), then \(\frac{d y}{d x}\)
is

1 \(\frac{-5}{1+25 \mathrm{x}^{2}}\)
2 \(\frac{5}{1+25 \mathrm{x}^{2}}\)
3 \(\frac{5}{1-25 \mathrm{x}^{2}}\)
4 0
MHT CET-2013
Limits, Continuity and Differentiability

80317 Derivative of \(\tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right)\) with respect to \(\sin ^{-1}\left(3 x-4 x^{3}\right)\) is

1 \(\frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
2 \(\frac{3}{\sqrt{1-\mathrm{x}^{2}}}\)
3 3
4 \(\frac{1}{3}\)
MHT CET-2016
Limits, Continuity and Differentiability

80318 Derivative of \(\log (\sec \theta+\tan \theta)\) with respect to
\(\sec \theta\) at \(\theta=\frac{\pi}{4}\) is

1 0
2 1
3 \(\frac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
MHT CET-2016
For More Updates join with Us