The Total solution for NCERT class 6-12
Differentiate eachof the following from first principles:(i) 2/x(ii) 1/√x
(iii) 1/x3
(iv) [x2 +1]/ x
(v) [x2 –1] / x
Answer - 1 : -
∴ Derivativeof f(x) = 1/√x is -1/2 x-3/2
Given:
f (x) = 1/x3
By using the formula,
∴Derivative of f(x) = 1/x3 is -3x-4
(iv) [x2 + 1]/ x
f (x) = [x2 + 1]/x
= 1 – 1/x2
∴Derivative of f(x) = 1 – 1/x2
(v) [x2 – 1] / x
f (x) = [x2 – 1]/x
Differentiate eachof the following from first principles:
(i) e-x
(ii) e3x
(iii) eax+b
Answer - 2 : -
f (x) = e-x
f (x) = e3x
f (x) = eax+b
Answer - 3 : -
(ii) sin x/x
f (x) = sin x/x
Differentiate thefollowing from first principles:
(i) tan2 x
(ii) tan (2x + 1)
Answer - 4 : -
f (x) = tan2 x
(ii) tan (2x+ 1)
f (x) = tan (2x + 1)
Answer - 5 : -
(ii) cos √x
f (x) = cos √x
f (x + h) = cos √(x+h)