3 3 d 7 x 2 x3 (e ) e 7 x 2 x (7 6 x 2 ) (7 6 x 2 )e 7 x 2 x dx
7. g `( x )
d d ¤ 100 ³ 100 (e 0.5t ) 100e 0.5t (0.5) 50e 0.5t ¥ 0.5t ´ dt dt ¦ e µ d 2t 1 9. g `(t ) 2500 (e ) 2500e 2t 1 (2) 5000e 2t 1 dt
8. f `(t )
1
10. f `( x )
6·2
2P
1. f `( x ) 20 2. y `
d
dx ¤¥¦ e
2
x2
2 2 x 1 x x ³ e 2 ( x ) e 2 ´µ 2P 2P
1 20 d (ln x ) 20 dx x x
1 1 d (ln 3x ) (3) 3x dx x
3 1 d [ln(5 x 3 )] 3 (15 x 2 ) dx x 5x 12 1 d 4. y ` 4 [ln(5 x 3 )] 4 3 (15 x 2 ) dx x 5x 3. g `( x )
3 1 d [ln( 10 x 3 )] ( 30 x 2 ) 3 dx x 10 x
5. h `( x )
6. f `( x ) 15 7. g `( x )
7 6x 2 1 d 2 7 6 [ln(7 x 2 x 3 )] ( x ) dx 7 x 2x 3 7 x 2x 3
8. f `(t )
6t 5 1 d [ln(3t 2 5t 20)] 2 (6t 5) 2 dt 3t 5t 20 3t 5t 20
9. g `(t )
d d [ln(e t )] (t ) 1 dt dt
10. f `( x )
6·3
1 d d 2 10 ( x ) 10 (ln x ) 15 (2 x ) 10 30 x dx x dx x
d 1 1 1 [ln(ln x )] dx ln x x x ln x
1. f `( x ) 20 2. y `
d x (3 ) 20(ln 3)(3x ) dx
d 3x (5 ) (ln 5)(53 x )(3) 3(ln 5)(53 x ) dx
3. g `( x )
3 d 5x3 (2 ) 15 x 2 (ln 2)(25 x ) dx
4. y ` 4 5. h `( x )
3 d 5x3 (2 ) 60 x 2 (ln 2)(25 x ) dx
3 d 10 x 3 (4 ) 30 x 2 (ln 4 )(4 10 x ) dx
6. f `( x ) 15 7. g `( x )
d d 2 ( x ) 10 (53 x ) 15 (2 x ) 10(ln 5)(53 x ) 3 30 x 30(ln 5)(53 x ) dx dx
3 d 7 x 2 x3 (3 ) (ln 3)(37 x 2 x )(7 6 x 2 ) dx
8. f `(t ) 100
130
Worked solutions
d (100.5t ) 100(ln10)(100.5t )(0.5) 50(ln10)(100.5t ) dt