Created by T Madas Question Differentiate the following expressions with respect to x a) y = x − x dy −2 −1 = 2x − x 3 dx b) y = x − x3 dy −1 = x − 6x dx c) y = x + d) y = x x − e) y = x + x2 x2 x dy −3 = − x − x −3 dx dy 12 = x + x −3 dx dy −1 −3 = 2x − x dx Created by T Madas Created by T Madas Question Find f ′ ( x ) for each of the following functions a) f ( x) = x 3 b) f ( x ) = x − c) f ( x) = 2x − x x d) f ( x ) = x − e) f ′ ( x ) = −6 x −4 + 10 x + 5x f ( x ) = x3 − − 14 − 13 + x −5 f ′( x ) = 6x +4 x +2 f ′ ( x ) = + x −3 + x 3 − f ′ ( x ) = x + x −4 2 f ′ ( x ) = x + x −3 2x 1 2x Created by T Madas − 12 Created by T Madas Question Differentiate the following expressions with respect to x a) y = b) y = c) y = x − 4x2 3x − dy −3 = x − 12 x −4 dx dy −7 = 30 x − x −3 dx 12 x2 x x3 + + 3x x ( d) y = x x − x ( e) y = + x ) dy −3 = − x −2 + x − x 3 dx ) dy = 21x − x dx dy −1 = 6x + dx Created by T Madas