Bài tập Toán DIFFERENTIATION 07

Created by T Madas Question Find f ′ ( x ) for each of the following functions a) f ( x) = x b) f ( x ) = c) ( x + x −4 ) f ′ ( x ) = x − x −4 2   − 2 x  x 4x  f ′ ( x ) = −3 x 7  f ( x) = 4x  −  x x 5  d) f ( x ) = x  + x  x  e) f ( x) = Created by T Madas + 15 x − 72 f ′ ( x ) = 36 x − 60 x f ′ ( x ) = −5 x  x3 − x     4x  x2  − 52 f ′( x) = x − 32 − 12 + 5x +5x − 32 Created by T Madas Question Differentiate the following expressions with respect to x a) y = ( x − 1)( 3x − ) dy − 12 − 32 − 52 = x + x − x dx 2x b) (3 + x ) y= dy −3 = − x − x −2 dx 4x c) y = d) x3 + x5 x dy = x + x2 dx x + x ) ( x − 3) ( y= dy −1 = x + 10 x − x dx 3 x  x 12 + x − 12   x 32 − x − 12       e) y =  3x dy −2 = x + x −3 + dx Created by T Madas Created by T Madas TANGENTS & NORMALS Created by T Madas