Differentiation of Function
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Limits, Continuity and Differentiability

80285 If \(x=a \sin t-b \cos t\) and \(y=a \cos t+b \sin t\), then \(y^{3} \frac{d^{2} y}{d^{2}}+x^{2}+y^{2}=\)

1 -1
2 1
3 2
4 0
MHT CET-2020
Limits, Continuity and Differentiability

80286 If \(y=\log \left[a^{3 x}\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]\), then \(\frac{d y}{d x}=\)

1 \(3+\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
2 \(\frac{3}{\log a}-\frac{3}{4(5-x)}-\frac{3}{(4 x+4)}\)
3 \(\frac{3}{\mathrm{a}}+\frac{3}{4(5-\mathrm{x})}-\frac{3}{4(\mathrm{x}+4)}\)
4 \(3 \log a-\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
MHT CET-2020
Limits, Continuity and Differentiability

80287 If \(y=x^{x^{x}}, \frac{d y}{d x}=y \cdot g(x)\), then \(g(x)=\)

1 \(\left[e^{x}+e^{x} \cdot x \cdot(1+\log x)\right]\)
2 \(\left[e^{x}-e^{x} \cdot x \cdot(1+\log x)\right]\)
3 \(\left[\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
4 \(\left[\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
MHT CET-2020
Limits, Continuity and Differentiability

80288 If \(\sin \left(\frac{x+y}{x-y}\right)=\tan \frac{\pi}{5}\), then \(\frac{d y}{d x}=\)

1 \(\frac{y}{x}\)
2 \(-\frac{y}{x}\)
3 \(-\frac{x}{y}\)
4 \(\frac{x}{y}\)
MHT CET-2020
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Limits, Continuity and Differentiability

80285 If \(x=a \sin t-b \cos t\) and \(y=a \cos t+b \sin t\), then \(y^{3} \frac{d^{2} y}{d^{2}}+x^{2}+y^{2}=\)

1 -1
2 1
3 2
4 0
MHT CET-2020
Limits, Continuity and Differentiability

80286 If \(y=\log \left[a^{3 x}\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]\), then \(\frac{d y}{d x}=\)

1 \(3+\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
2 \(\frac{3}{\log a}-\frac{3}{4(5-x)}-\frac{3}{(4 x+4)}\)
3 \(\frac{3}{\mathrm{a}}+\frac{3}{4(5-\mathrm{x})}-\frac{3}{4(\mathrm{x}+4)}\)
4 \(3 \log a-\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
MHT CET-2020
Limits, Continuity and Differentiability

80287 If \(y=x^{x^{x}}, \frac{d y}{d x}=y \cdot g(x)\), then \(g(x)=\)

1 \(\left[e^{x}+e^{x} \cdot x \cdot(1+\log x)\right]\)
2 \(\left[e^{x}-e^{x} \cdot x \cdot(1+\log x)\right]\)
3 \(\left[\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
4 \(\left[\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
MHT CET-2020
Limits, Continuity and Differentiability

80288 If \(\sin \left(\frac{x+y}{x-y}\right)=\tan \frac{\pi}{5}\), then \(\frac{d y}{d x}=\)

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

80285 If \(x=a \sin t-b \cos t\) and \(y=a \cos t+b \sin t\), then \(y^{3} \frac{d^{2} y}{d^{2}}+x^{2}+y^{2}=\)

1 -1
2 1
3 2
4 0
MHT CET-2020
Limits, Continuity and Differentiability

80286 If \(y=\log \left[a^{3 x}\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]\), then \(\frac{d y}{d x}=\)

1 \(3+\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
2 \(\frac{3}{\log a}-\frac{3}{4(5-x)}-\frac{3}{(4 x+4)}\)
3 \(\frac{3}{\mathrm{a}}+\frac{3}{4(5-\mathrm{x})}-\frac{3}{4(\mathrm{x}+4)}\)
4 \(3 \log a-\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
MHT CET-2020
Limits, Continuity and Differentiability

80287 If \(y=x^{x^{x}}, \frac{d y}{d x}=y \cdot g(x)\), then \(g(x)=\)

1 \(\left[e^{x}+e^{x} \cdot x \cdot(1+\log x)\right]\)
2 \(\left[e^{x}-e^{x} \cdot x \cdot(1+\log x)\right]\)
3 \(\left[\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
4 \(\left[\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
MHT CET-2020
Limits, Continuity and Differentiability

80288 If \(\sin \left(\frac{x+y}{x-y}\right)=\tan \frac{\pi}{5}\), then \(\frac{d y}{d x}=\)

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

80285 If \(x=a \sin t-b \cos t\) and \(y=a \cos t+b \sin t\), then \(y^{3} \frac{d^{2} y}{d^{2}}+x^{2}+y^{2}=\)

1 -1
2 1
3 2
4 0
MHT CET-2020
Limits, Continuity and Differentiability

80286 If \(y=\log \left[a^{3 x}\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]\), then \(\frac{d y}{d x}=\)

1 \(3+\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
2 \(\frac{3}{\log a}-\frac{3}{4(5-x)}-\frac{3}{(4 x+4)}\)
3 \(\frac{3}{\mathrm{a}}+\frac{3}{4(5-\mathrm{x})}-\frac{3}{4(\mathrm{x}+4)}\)
4 \(3 \log a-\frac{3}{4(5-x)}-\frac{3}{4(x+4)}\)
MHT CET-2020
Limits, Continuity and Differentiability

80287 If \(y=x^{x^{x}}, \frac{d y}{d x}=y \cdot g(x)\), then \(g(x)=\)

1 \(\left[e^{x}+e^{x} \cdot x \cdot(1+\log x)\right]\)
2 \(\left[e^{x}-e^{x} \cdot x \cdot(1+\log x)\right]\)
3 \(\left[\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
4 \(\left[\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{\mathrm{x}}(\mathrm{x}+1) \log \mathrm{x}\right]\)
MHT CET-2020
Limits, Continuity and Differentiability

80288 If \(\sin \left(\frac{x+y}{x-y}\right)=\tan \frac{\pi}{5}\), then \(\frac{d y}{d x}=\)

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