Differentiation of Function
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Limits, Continuity and Differentiability

80249 If \(x=\frac{1-t^{2}}{1+t^{2}}\) and \(y=\frac{2 t}{1+t^{2}}\) then \(\frac{d y}{d x}\)

1 \(-y / x\)
2 \(y / x\)
3 \(-x / y\)
4 \(x / y\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80250 If \(\sin y=x \sin (a+y)\), then \(\frac{d y}{d x}=\)

1 \(\frac{\sin \sqrt{a}}{\sin (a+y)}\)
2 \(\frac{\sin ^{2}(a+y)}{\sin a}\)
3 \(\frac{\sin (a+y)}{\sin a}\)
4 \(\frac{\cos (a+y)}{\cos a}\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80251 If \(x=A \cos 4 t+B \sin 4 t\) then \(\frac{d^{2} x}{d t^{2}}\) is equal to :

1 \(-16 x\)
2 \(16 x\)
3 \(\mathrm{x}\)
4 \(-x\)
Karnataka CET-2004
Limits, Continuity and Differentiability

80252 The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\) when \(\mathbf{y}(\mathbf{1})=\mathbf{2}\) is

1 three
2 one
3 infinite
4 two
Karnataka CET-2021
Limits, Continuity and Differentiability

80253 If \(y=(x-1)^{2}(x-2)^{3}(x-3)^{5}\), then \(\frac{d y}{d x}\) at \(x=4\) is equal to

1 108
2 54
3 36
4 516
Karnataka CET-2021
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

80249 If \(x=\frac{1-t^{2}}{1+t^{2}}\) and \(y=\frac{2 t}{1+t^{2}}\) then \(\frac{d y}{d x}\)

1 \(-y / x\)
2 \(y / x\)
3 \(-x / y\)
4 \(x / y\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80250 If \(\sin y=x \sin (a+y)\), then \(\frac{d y}{d x}=\)

1 \(\frac{\sin \sqrt{a}}{\sin (a+y)}\)
2 \(\frac{\sin ^{2}(a+y)}{\sin a}\)
3 \(\frac{\sin (a+y)}{\sin a}\)
4 \(\frac{\cos (a+y)}{\cos a}\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80251 If \(x=A \cos 4 t+B \sin 4 t\) then \(\frac{d^{2} x}{d t^{2}}\) is equal to :

1 \(-16 x\)
2 \(16 x\)
3 \(\mathrm{x}\)
4 \(-x\)
Karnataka CET-2004
Limits, Continuity and Differentiability

80252 The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\) when \(\mathbf{y}(\mathbf{1})=\mathbf{2}\) is

1 three
2 one
3 infinite
4 two
Karnataka CET-2021
Limits, Continuity and Differentiability

80253 If \(y=(x-1)^{2}(x-2)^{3}(x-3)^{5}\), then \(\frac{d y}{d x}\) at \(x=4\) is equal to

1 108
2 54
3 36
4 516
Karnataka CET-2021
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Limits, Continuity and Differentiability

80249 If \(x=\frac{1-t^{2}}{1+t^{2}}\) and \(y=\frac{2 t}{1+t^{2}}\) then \(\frac{d y}{d x}\)

1 \(-y / x\)
2 \(y / x\)
3 \(-x / y\)
4 \(x / y\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80250 If \(\sin y=x \sin (a+y)\), then \(\frac{d y}{d x}=\)

1 \(\frac{\sin \sqrt{a}}{\sin (a+y)}\)
2 \(\frac{\sin ^{2}(a+y)}{\sin a}\)
3 \(\frac{\sin (a+y)}{\sin a}\)
4 \(\frac{\cos (a+y)}{\cos a}\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80251 If \(x=A \cos 4 t+B \sin 4 t\) then \(\frac{d^{2} x}{d t^{2}}\) is equal to :

1 \(-16 x\)
2 \(16 x\)
3 \(\mathrm{x}\)
4 \(-x\)
Karnataka CET-2004
Limits, Continuity and Differentiability

80252 The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\) when \(\mathbf{y}(\mathbf{1})=\mathbf{2}\) is

1 three
2 one
3 infinite
4 two
Karnataka CET-2021
Limits, Continuity and Differentiability

80253 If \(y=(x-1)^{2}(x-2)^{3}(x-3)^{5}\), then \(\frac{d y}{d x}\) at \(x=4\) is equal to

1 108
2 54
3 36
4 516
Karnataka CET-2021
For More Updates join with Us
Limits, Continuity and Differentiability

80249 If \(x=\frac{1-t^{2}}{1+t^{2}}\) and \(y=\frac{2 t}{1+t^{2}}\) then \(\frac{d y}{d x}\)

1 \(-y / x\)
2 \(y / x\)
3 \(-x / y\)
4 \(x / y\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80250 If \(\sin y=x \sin (a+y)\), then \(\frac{d y}{d x}=\)

1 \(\frac{\sin \sqrt{a}}{\sin (a+y)}\)
2 \(\frac{\sin ^{2}(a+y)}{\sin a}\)
3 \(\frac{\sin (a+y)}{\sin a}\)
4 \(\frac{\cos (a+y)}{\cos a}\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80251 If \(x=A \cos 4 t+B \sin 4 t\) then \(\frac{d^{2} x}{d t^{2}}\) is equal to :

1 \(-16 x\)
2 \(16 x\)
3 \(\mathrm{x}\)
4 \(-x\)
Karnataka CET-2004
Limits, Continuity and Differentiability

80252 The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\) when \(\mathbf{y}(\mathbf{1})=\mathbf{2}\) is

1 three
2 one
3 infinite
4 two
Karnataka CET-2021
Limits, Continuity and Differentiability

80253 If \(y=(x-1)^{2}(x-2)^{3}(x-3)^{5}\), then \(\frac{d y}{d x}\) at \(x=4\) is equal to

1 108
2 54
3 36
4 516
Karnataka CET-2021
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

80249 If \(x=\frac{1-t^{2}}{1+t^{2}}\) and \(y=\frac{2 t}{1+t^{2}}\) then \(\frac{d y}{d x}\)

1 \(-y / x\)
2 \(y / x\)
3 \(-x / y\)
4 \(x / y\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80250 If \(\sin y=x \sin (a+y)\), then \(\frac{d y}{d x}=\)

1 \(\frac{\sin \sqrt{a}}{\sin (a+y)}\)
2 \(\frac{\sin ^{2}(a+y)}{\sin a}\)
3 \(\frac{\sin (a+y)}{\sin a}\)
4 \(\frac{\cos (a+y)}{\cos a}\)
Karnataka CET-2000
Limits, Continuity and Differentiability

80251 If \(x=A \cos 4 t+B \sin 4 t\) then \(\frac{d^{2} x}{d t^{2}}\) is equal to :

1 \(-16 x\)
2 \(16 x\)
3 \(\mathrm{x}\)
4 \(-x\)
Karnataka CET-2004
Limits, Continuity and Differentiability

80252 The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\) when \(\mathbf{y}(\mathbf{1})=\mathbf{2}\) is

1 three
2 one
3 infinite
4 two
Karnataka CET-2021
Limits, Continuity and Differentiability

80253 If \(y=(x-1)^{2}(x-2)^{3}(x-3)^{5}\), then \(\frac{d y}{d x}\) at \(x=4\) is equal to

1 108
2 54
3 36
4 516
Karnataka CET-2021