Created by T Madas Question Find f ′ ( x ) for each of the following functions f ′ ( x ) = 12 x − a) f ( x ) = x3 − x + b) f ( x ) = x − 12 f ′ ( x ) = −3 x + 2x − 32 +2 f ′ ( x ) = x3 + x c) f ( x ) = x + x − d) f ( x ) = x − x 2 f ′( x) = x + 6x e) f ( x ) = x + x f ′( x) = x Created by T Madas − 23 − 52 +5 Created by T Madas Question Differentiate each of the following functions with respect to x a) f ( x) = 6x − 32 f ′ ( x ) = −9 x + 4x +1 − 52 +4 b) g ( x ) = x − x −1 g ′ ( x ) = x3 + x −2 c) h ( x ) = x − x h′ ( x ) = 18 x − x3 1 d) p ( x ) = x − x + x ( e) v ( x ) = x + ) − 14 p′ ( x ) = x − 12 − 2x v′ ( x ) = 128 x + Created by T Madas − 32 −1x − 45 Created by T Madas Question Carry out the following differentiations a) d 4t − 7t + dt b) d 12 − 12 y −3y dy c) d z − z −1 + z dz d) d −3 w −w dw d −3 − w − w = 2w + w dw e) d ax − x dx d ax − x = 2ax − x dx ( ( ( ) d 4t − 7t + = 8t − dt ( ) ) d 12 − 12 − 12 − 23 y −3y = 2y +3y dy ) d z − z −1 + z = z + z −2 + dz ( ( Created by T Madas ) ) ... = 128 x + Created by T Madas − 32 −1x − 45 Created by T Madas Question Carry out the following differentiations a) d 4t − 7t + dt b) d 12 − 12 y −3y dy c) d z − z −1 + z dz d) d