# NCERT Solutions For Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 5 |

Exercise | Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.4 |

Number of Questions Solved |

## NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4

**NCERT TEXTBOOK EXERCISES**

**Ex 5.4 Class 12 Maths Question 1.**

$y=\frac { { e }^{ x } }{ sinx }$

**Solution:**

$y=\frac { { e }^{ x } }{ sinx }$

for y =u/v,

$\frac { dy }{ dx } =\frac { { e }^{ x }{ sin }x-{ e }^{ x }cosx }{ { sin }^{ 2 }x }$

$or\frac { dy }{ dx } =\frac { { e }^{ x }{ sin }x-{ e }^{ x }cosx }{ { sin }^{ 2 }x } ,where\quad x\neq n\pi ,x\in z$

**Ex 5.4 Class 12 Maths Question 2.**

${ e }^{ { sin }^{ -1 }x }$

**Solution:**

${ e }^{ { sin }^{ -1 }x }$

$y={ e }^{ { sin }^{ -1 }x }$

x=sint

**Ex 5.4 Class 12 Maths Question 3.**

${ e }^{ { x }^{ 3 } }=y$

**Solution:**

${ e }^{ { x }^{ 3 } }=y$

**Ex 5.4 Class 12 Maths Question 4.**

$sin\left( { tan }^{ -1 }{ e }^{ -x } \right) =y$

**Solution:**

$sin\left( { tan }^{ -1 }{ e }^{ -x } \right) =y$

$\frac { dy }{ dx } =cos\left( { tan }^{ -1 }{ e }^{ -x } \right) \frac { d }{ dx } \left( { tan }^{ -1 }{ e }^{ -x } \right)$

$=cos\left( { tan }^{ -1 }{ e }^{ -x } \right) \frac { 1 }{ 1+{ e }^{ -2x } } \frac { d }{ dx } \left( { e }^{ -x } \right)$

$=-cos\left( { tan }^{ -1 }{ e }^{ -x } \right) \frac { 1 }{ 1+{ e }^{ -2x } } .\left( { e }^{ -x } \right)$

**Ex 5.4 Class 12 Maths Question 5.**

$log(cos\quad { e }^{ x })=y$

**Solution:**

$\frac { dy }{ dx } =\frac { 1 }{ cos\quad { e }^{ x } } \left( -sin{ e }^{ x } \right) .{ e }^{ x }\quad =-tan\left( { e }^{ x } \right)$

**Ex 5.4 Class 12 Maths Question 6.**

ex+ex^{2}+â€¦+ex^{5}=y^{(say)}

**Solution:**

$let\quad u={ e }^{ { x }^{ n } },put\quad { x }^{ n }=t,u={ e }^{ t },t={ x }^{ n }$

ex+ex^{2}+â€¦+ex^{5}=y^{(say)}

**Ex 5.4 Class 12 Maths Question 7.**

$\sqrt { { e }^{ \sqrt { x } } } ,x>0$

**Solution:**

y = $\sqrt { { e }^{ \sqrt { x } } } ,x>0$

$y=\sqrt { { e }^{ \sqrt { x } } } ,let\quad y=\sqrt { s } ,s={ e }^{ t },t=\sqrt { x }$

**Ex 5.4 Class 12 Maths Question 8.**

log(log x),x>1

**Solution:**

y = log(log x),

put y = log t, t = log x,

differentiating

**Ex 5.4 Class 12 Maths Question 9.**

$\frac { cosx }{ logx } =y(say),x>0$

**Solution:**

Let $y=\frac { cosx }{ logx }$

**Ex 5.4 Class 12 Maths Question 10.**

cos(log x+e^{x}),x>0

**Solution:**

y = cos(log x+e^{x}),x>0

put y = cos t,t = log x+e^{x}

## NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.4 PDF

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### Other Chapter of Class 12 Maths Chapter 5 Continuity and Differentiability

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