Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.1 Improve Improve Improve Like Article Like Save Article Save Share Report issue Report 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 Last Updated : 07 Apr, 2021 Like Article Save Article Previous Class 12 RD Sharma Solutions - Chapter 10 Differentiability - Exercise 10.2 Next Class 12 RD Sharma Solutions - Chapter 11 Differentiation - Exercise 11.2 | Set 1 Share your thoughts in the comments Add Your Comment Please Login to comment...