=lim
δx→ 0
+δx
=
8.1.3 Standard derivatives ➤232 243➤➤
Give the derivatives of the following functions
(i) 49 (ii) x^4 (iii)
√
x (iv)
1
x^2
(v) sinx (vi) ex (vii) lnx (viii) 2x
8.1.4 Rules of differentiation ➤234 244➤➤
Differentiate and simplify
(i) 3x^4 − 2 x^2 + 3 x− 1 (ii) x^2 cosx
(iii)
x− 1
x+ 1
(iv) cos(x^2 + 1 )
(v) ln 3x (vi) e−^2 x
(vii)
√
x^2 − 1
8.1.5 Implicit differentiation ➤238 244➤➤
A.Ifx^2 + 2 xy+ 2 y^2 =1 obtain
dy
dx
as a function ofxandy.
B. Obtain the derivative of sin−^1 xby using implicit differentiation.
C.Differentiatey= 2 x.
D.Iff(x)=
x− 1
x+ 2
evaluatef′( 1 ).
8.1.6 Parametric differentiation ➤240 245➤➤
Ifx= 3 t^2 ,y=cos(t+ 1 )evaluate
dy
dx
as a function oft.
8.1.7 Higher order derivatives ➤241 245➤➤
A.Evaluate the second derivative of each of the following functions:
(i) 2x+ 1 (ii) x^3 − 2 x+ 1
(iii) e−xcosx (iv)
x+ 1
(x− 1 )(x+ 2 )