11th Maths Monthly Test - 4 ( Differential Calculus - Differentiability and Methods of Differentiat

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Differential Calculus - Differentiability and Methods of Differentiat-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

If sin y=x sin (a+y),then prove that \({dy\over dx}={sin^2(a+y)\over sin \ a}, a\neq n \pi.\)

Find the derivatives of the following functions with respect to corresponding independent variables:y = cosec x. cot x

If y = tan^-1\(({1+x\over 1-x}),find \ y'\)

Discuss the differentiability of \(f\left( x \right) =\begin{cases} x{ e }^{ -\left( \frac { 1 }{ \left| x \right| } +\frac { 1 }{ x } \right) } \\ 0,\quad \quad \quad \quad x=0 \end{cases},\quad x\neq 0\) at x=0

If \(y=\sqrt { \frac { 1+{ e }^{ x } }{ 1-{ e }^{ x } } } ,\) show that \(\frac { dy }{ dx } =\frac { { e }^{ x } }{ (1-{ e }^{ x })\sqrt { 1-{ e }^{ 2x } } } \)

Find the derivatives of the following functions with respect to corresponding independent variables:y =log₁₀x

Differentiate the following:\(y={e^{3x}\over 1+e^x}\)

Find \({d^2y\over dx^2}\) if x²+y²=4.

Find the derivation
(3 see x - 4 cosec x) (2 sin x + 5 cos x)

Differentiate the following: y=sin (tan(\(\sqrt{sin x}\)))

Differentiate the following: y=e^xcosx

If y=e^tan-1x, Show that (1+x²)y"+(2x-1)y'=0.

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11th Maths Monthly Test - 4 ( Differential Calculus - Differentiability and Methods of Differentiat

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Differential Calculus - Differentiability and Methods of Differentiat-Aug 2020

Part - A

Generic 5 - Answer All Question

If sin y=x sin (a+y),then prove that \({dy\over dx}={sin^2(a+y)\over sin \ a}, a\neq n \pi.\)

Find the derivatives of the following functions with respect to corresponding independent variables:y = cosec x. cot x

If y = tan-1\(({1+x\over 1-x}),find \ y'\)

Discuss the differentiability of \(f\left( x \right) =\begin{cases} x{ e }^{ -\left( \frac { 1 }{ \left| x \right| } +\frac { 1 }{ x } \right) } \\ 0,\quad \quad \quad \quad x=0 \end{cases},\quad x\neq 0\) at x=0

If \(y=\sqrt { \frac { 1+{ e }^{ x } }{ 1-{ e }^{ x } } } ,\) show that \(\frac { dy }{ dx } =\frac { { e }^{ x } }{ (1-{ e }^{ x })\sqrt { 1-{ e }^{ 2x } } } \)

Find the derivatives of the following functions with respect to corresponding independent variables:y =log10x

Differentiate the following:\(y={e^{3x}\over 1+e^x}\)

Find \({d^2y\over dx^2}\) if x2+y2=4.

Find the derivation (3 see x - 4 cosec x) (2 sin x + 5 cos x)

Differentiate the following: y=sin (tan(\(\sqrt{sin x}\)))

Differentiate the following: y=excosx

If y=etan-1x, Show that (1+x2)y"+(2x-1)y'=0.

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If y = tan^-1\(({1+x\over 1-x}),find \ y'\)

Find the derivatives of the following functions with respect to corresponding independent variables:y =log₁₀x

Find \({d^2y\over dx^2}\) if x²+y²=4.

Find the derivation
(3 see x - 4 cosec x) (2 sin x + 5 cos x)

Differentiate the following: y=e^xcosx

If y=e^tan-1x, Show that (1+x²)y"+(2x-1)y'=0.