Differentiation of Function
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Limits, Continuity and Differentiability

80280 The derivative
\(\sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)\) w.r.t. \(\cos ^{-1} x\) is

1 \(-\frac{1}{2}\)
2 1
3 -1
4 \(\frac{1}{2}\)
MHT CET-2020
Limits, Continuity and Differentiability

80281 If \(f^{\prime}(x)=k(\cos x-\sin x), f^{\prime}(0)=3, f\left(\frac{\pi}{2}\right)=15\) then \(\mathbf{f}(\mathbf{x})=\)

1 \(-3(\sin x+\cos x)-12\)
2 \(3(\sin x+\cos x)+12\)
3 \(12(\sin x+\cos x)+3\)
4 \(3(\sin x+\cos x)-12\)
MHT CET-2020
Limits, Continuity and Differentiability

80282 The derivative of \(\cot ^{-1} x\) w.r.t. \(\log \left(1+x^{2}\right)\) is

1 \(2 x\)
2 \(\frac{1}{2 \mathrm{x}}\)
3 \(-\frac{1}{2 x}\)
4 \(-2 x\)
MHT CET-2020
Limits, Continuity and Differentiability

80283 If \(y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]\), then \(\frac{d y}{d x}=\)

1 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{\mathrm{x}^{2}}-1}\)
2 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
3 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
4 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{\mathrm{x}^{2}-1}}\)
MHT CET-2020
Limits, Continuity and Differentiability

80284 If \(x^{2} y^{2}=\sin ^{-1} \sqrt{x^{2}+y^{2}}+\cos ^{-1} \sqrt{x^{2}+y^{2}}\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{y}\)
2 \(\frac{y}{x}\)
3 \(\frac{x}{y}\)
4 \(\frac{-y}{x}\)
MHT CET-2020
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

80280 The derivative
\(\sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)\) w.r.t. \(\cos ^{-1} x\) is

1 \(-\frac{1}{2}\)
2 1
3 -1
4 \(\frac{1}{2}\)
MHT CET-2020
Limits, Continuity and Differentiability

80281 If \(f^{\prime}(x)=k(\cos x-\sin x), f^{\prime}(0)=3, f\left(\frac{\pi}{2}\right)=15\) then \(\mathbf{f}(\mathbf{x})=\)

1 \(-3(\sin x+\cos x)-12\)
2 \(3(\sin x+\cos x)+12\)
3 \(12(\sin x+\cos x)+3\)
4 \(3(\sin x+\cos x)-12\)
MHT CET-2020
Limits, Continuity and Differentiability

80282 The derivative of \(\cot ^{-1} x\) w.r.t. \(\log \left(1+x^{2}\right)\) is

1 \(2 x\)
2 \(\frac{1}{2 \mathrm{x}}\)
3 \(-\frac{1}{2 x}\)
4 \(-2 x\)
MHT CET-2020
Limits, Continuity and Differentiability

80283 If \(y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]\), then \(\frac{d y}{d x}=\)

1 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{\mathrm{x}^{2}}-1}\)
2 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
3 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
4 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{\mathrm{x}^{2}-1}}\)
MHT CET-2020
Limits, Continuity and Differentiability

80284 If \(x^{2} y^{2}=\sin ^{-1} \sqrt{x^{2}+y^{2}}+\cos ^{-1} \sqrt{x^{2}+y^{2}}\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{y}\)
2 \(\frac{y}{x}\)
3 \(\frac{x}{y}\)
4 \(\frac{-y}{x}\)
MHT CET-2020
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Limits, Continuity and Differentiability

80280 The derivative
\(\sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)\) w.r.t. \(\cos ^{-1} x\) is

1 \(-\frac{1}{2}\)
2 1
3 -1
4 \(\frac{1}{2}\)
MHT CET-2020
Limits, Continuity and Differentiability

80281 If \(f^{\prime}(x)=k(\cos x-\sin x), f^{\prime}(0)=3, f\left(\frac{\pi}{2}\right)=15\) then \(\mathbf{f}(\mathbf{x})=\)

1 \(-3(\sin x+\cos x)-12\)
2 \(3(\sin x+\cos x)+12\)
3 \(12(\sin x+\cos x)+3\)
4 \(3(\sin x+\cos x)-12\)
MHT CET-2020
Limits, Continuity and Differentiability

80282 The derivative of \(\cot ^{-1} x\) w.r.t. \(\log \left(1+x^{2}\right)\) is

1 \(2 x\)
2 \(\frac{1}{2 \mathrm{x}}\)
3 \(-\frac{1}{2 x}\)
4 \(-2 x\)
MHT CET-2020
Limits, Continuity and Differentiability

80283 If \(y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]\), then \(\frac{d y}{d x}=\)

1 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{\mathrm{x}^{2}}-1}\)
2 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
3 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
4 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{\mathrm{x}^{2}-1}}\)
MHT CET-2020
Limits, Continuity and Differentiability

80284 If \(x^{2} y^{2}=\sin ^{-1} \sqrt{x^{2}+y^{2}}+\cos ^{-1} \sqrt{x^{2}+y^{2}}\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{y}\)
2 \(\frac{y}{x}\)
3 \(\frac{x}{y}\)
4 \(\frac{-y}{x}\)
MHT CET-2020
For More Updates join with Us
Limits, Continuity and Differentiability

80280 The derivative
\(\sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)\) w.r.t. \(\cos ^{-1} x\) is

1 \(-\frac{1}{2}\)
2 1
3 -1
4 \(\frac{1}{2}\)
MHT CET-2020
Limits, Continuity and Differentiability

80281 If \(f^{\prime}(x)=k(\cos x-\sin x), f^{\prime}(0)=3, f\left(\frac{\pi}{2}\right)=15\) then \(\mathbf{f}(\mathbf{x})=\)

1 \(-3(\sin x+\cos x)-12\)
2 \(3(\sin x+\cos x)+12\)
3 \(12(\sin x+\cos x)+3\)
4 \(3(\sin x+\cos x)-12\)
MHT CET-2020
Limits, Continuity and Differentiability

80282 The derivative of \(\cot ^{-1} x\) w.r.t. \(\log \left(1+x^{2}\right)\) is

1 \(2 x\)
2 \(\frac{1}{2 \mathrm{x}}\)
3 \(-\frac{1}{2 x}\)
4 \(-2 x\)
MHT CET-2020
Limits, Continuity and Differentiability

80283 If \(y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]\), then \(\frac{d y}{d x}=\)

1 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{\mathrm{x}^{2}}-1}\)
2 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
3 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
4 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{\mathrm{x}^{2}-1}}\)
MHT CET-2020
Limits, Continuity and Differentiability

80284 If \(x^{2} y^{2}=\sin ^{-1} \sqrt{x^{2}+y^{2}}+\cos ^{-1} \sqrt{x^{2}+y^{2}}\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{y}\)
2 \(\frac{y}{x}\)
3 \(\frac{x}{y}\)
4 \(\frac{-y}{x}\)
MHT CET-2020
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

80280 The derivative
\(\sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)\) w.r.t. \(\cos ^{-1} x\) is

1 \(-\frac{1}{2}\)
2 1
3 -1
4 \(\frac{1}{2}\)
MHT CET-2020
Limits, Continuity and Differentiability

80281 If \(f^{\prime}(x)=k(\cos x-\sin x), f^{\prime}(0)=3, f\left(\frac{\pi}{2}\right)=15\) then \(\mathbf{f}(\mathbf{x})=\)

1 \(-3(\sin x+\cos x)-12\)
2 \(3(\sin x+\cos x)+12\)
3 \(12(\sin x+\cos x)+3\)
4 \(3(\sin x+\cos x)-12\)
MHT CET-2020
Limits, Continuity and Differentiability

80282 The derivative of \(\cot ^{-1} x\) w.r.t. \(\log \left(1+x^{2}\right)\) is

1 \(2 x\)
2 \(\frac{1}{2 \mathrm{x}}\)
3 \(-\frac{1}{2 x}\)
4 \(-2 x\)
MHT CET-2020
Limits, Continuity and Differentiability

80283 If \(y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]\), then \(\frac{d y}{d x}=\)

1 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{\mathrm{x}^{2}}-1}\)
2 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
3 \(\left(\frac{1}{4}\right) \frac{1}{\sqrt{1-\mathrm{x}^{2}}}\)
4 \(\left(-\frac{1}{2}\right) \frac{1}{\sqrt{\mathrm{x}^{2}-1}}\)
MHT CET-2020
Limits, Continuity and Differentiability

80284 If \(x^{2} y^{2}=\sin ^{-1} \sqrt{x^{2}+y^{2}}+\cos ^{-1} \sqrt{x^{2}+y^{2}}\), then \(\frac{d y}{d x}=\)

1 \(\frac{-x}{y}\)
2 \(\frac{y}{x}\)
3 \(\frac{x}{y}\)
4 \(\frac{-y}{x}\)
MHT CET-2020