Please use First Principles to answer my question.

More DERIVliver 1. Differentiate each of the following functions d p with respect to x. - (a) y = 4x2(1 - x3) 5. Differentiate: (b) y = (3x + 4)(x2 - 5) 5X (a) y = 10 - x (c) y = (2x - 1)(8x2 - 3x + 1) (d) y = (1 - x)(1 + x2)(5 - x2) ( b) y = x3 - 3x Vx (e) y = (x2 - 3x - 1)(x3 + 4x - 3) 3 - x (c )y = 6+ x2 2. Find dy/dx: (a) y = (1 -3x)(x2 - 2)3 2x3 - 7x2 (9 - '0) (6, - 1) (3, 0.5) (d) y = - ( - 1, 2) (0'0) (I'I ) 3x 2 + 4 (b) y = (5 -2x)2 (x - 1)3 C2 + x 2 ( e ) y = x (1 - x2 ) ( 2 + x ) 3 (e) y = 2 _ 2 c is a constant of each of the following at the given point. 11. Find the equation of the tangent to the graph (d) y = (3x2 - 4x)2(7 - Vx) (1 + x9) 2 (f) y = 5x2 + 7 10 - x (e) y = XV x - 1 I+x . I+x (E - x2) (I + zx) = (x )! (3 ) 6. Differentiate: ' I1 = =1 - xxB+ zx (2) ' 1 = 1 - zzx + x (1) 9 - x9 = ( x ) / (p ) I- x = ( x ) ) (e ) 2x+= (x) (q) 3. Find f'(x ): (a) f(x) = xV/1 - 3x (a) E(x ) = 3 - 4x 2 ( b ) f ( x ) = (x - 1)V x+ 1 ( b ) f ( x ) = = V x2 - 1 ( c) f ( x ) = (x + 1)2 Vx2 + 1 (d) f (x) = (1 - 3x)Vx2 + 3x - 2 (c) f (x ) = Vx - 1 Vx + 1 (e ) 1(x ) = ( 1 + 2) (3-4) (d) f(x) = V3 - x2 X (f ) f ( x ) = (2x ) 13 ( x - 4 ) -213 ( e ) F(x ) = - a 2 + x 2 Voz _ a is a constant 4. Given that p and q are functions of x, find: a2b2c2 (c) x + y3 - 3axy = 0, a is a constant (8) 2V/x + 4Vy = Va, a is a constant 7: Find y' in each of the following cases: d (1) f(x) = ; a) (Px) ( x - a) (x - b) (x - c) "tox = = ( 1 + x ) - 2 ( 1 - x ) (a ) a, b, c are constants X = 21(