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# Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.1

• Last Updated : 07 Apr, 2021

### 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 e3x

Solution:

We have,

Let,

f(x)=e3x

f(x+h)=e3(x+h)     =3e3x

### Question 3. Differentiate the following functions from first principles eax+b

Solution:

We have,

Let,

f(x)=eax+b

f(x+h)=ea(x+h)+b     =aeax+b

### Question 4. Differentiate the following functions from first principles ecosx

Solution:

We have,

Let,

f(x)=ecosx

f(x+h)=ecos(x+h)        =ecosx(-sinx)

=-sinx.ecosx

### 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 x2ex

Solution:

We have,

Let,

f(x)=x2ex

f(x+h)=(x+h)2e(x+h)    Since, =x2ex+2xex+0

=ex(x2+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    My Personal Notes arrow_drop_up