Here we provide RD Sharma Class 12 Ex 11.1 Solutions Chapter 11 Differentiation for English medium students, Which will very helpful for every student in their exams. Students can download the RD Sharma Class 12 Ex 11.1 Solutions Chapter 11 Differentiation book pdf download. Now you will get step-by-step solutions to each question.

Textbook | NCERT |

Class | Class 12th |

Subject | Maths |

Chapter | 11 |

Exercise | 11.1 |

Category | RD Sharma Solutions |

**RD Sharma Class 12 Ex 11.1 Solutions Chapter 11 Differentiation**

**Question 1.** Differentiate the following functions from first principles e^{-x}

**Solution:**

We have,

Let,

f(x)=e^{-x}

f(x+h)=e^{-(x+h)}

=-e^{-x}

**Question 2. **Differentiate the following functions from first principles e^{3x}

**Solution:**

We have,

Let,

f(x)=e^{3x}

f(x+h)=e^{3(x+h)}

=3e^{3x}

**Question 3.** Differentiate the following functions from first principles e^{ax+b}

**Solution:**

We have,

Let,

f(x)=e^{ax+b}

f(x+h)=e^{a(x+h)+b}

=ae^{ax+b}

**Question 4.** Differentiate the following functions from first principles e^{cosx}

**Solution:**

We have,

Let,

f(x)=e^{cosx}

f(x+h)=e^{cos(x+h)}

=e^{cosx}(-sinx)

=-sinx.e^{cosx}

**Question 5.** Differentiate the following functions from first principles e^{√2x}

**Solution:**

We have,

Let,

f(x)=e^{√2x}

f(x+h)=e^{√2(x+h)}

(After rationalising the numerator)

**Question 6.** Differentiate the following functions from first principles log(cosx)

**Solution:**

We have,

Let,

f(x)=log(cosx)

f(x+h)=log(cos(x+h))

Since,

=-(2sinx)/(2cosx)

=-tanx

**Question 7.** Differentiate the following functions from first principles e^{√cotx}

**Solution:**

We have,

Let,

f(x)=e^{√cotx}

f(x+h)=e^{√cot(x+h)}

since,

(After rationalising the numerator)

Since,

**Question 8.** Differentiate the following functions from first principles x^{2}e^{x}

**Solution:**

We have,

Let,

f(x)=x^{2}e^{x}

f(x+h)=(x+h)^{2}e^{(x+h)}

Since,

=x^{2}e^{x}+2xe^{x}+0

=e^{x}(x^{2}+2x)

**Question 9.** Differentiate the following functions from first principles log(cosecx)

**Solution:**

We have,

Let,

f(x)=log(cosecx)

f(x+h)=log(cosec(x+h))

=-cotx

**Question 10.** Differentiate the following functions from first principles sin^{-1}(2x+3)

**Solution:**

We have,

Let,

f(x)=sin^{-1}(2x+3)

f(x+h)=sin^{-1}[2(x+h)+3]

f(x+h)=sin^{-1}(2x+2h+3)

Where

(After rationalising the numerator)

Solving above equation

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