Page 167 - ADVANCED MATH F.5

Form Five Form Five

Derivatives of exponential functions
Teaching steps

1. Guide students through discussions to deduce derivatives of
sin xx ⎣FOR ONLINE READING ONLY
exponential functions. Engage students in groups to perform
Activity 8.5 on recognizing the derivative of an exponential
function. Advise students to share their findings through
presentations.
2. Use Examples 8.46 to 8.49 in the Student’s Book to guide
students and assist them on how to find derivatives of
exponential functions. Engage students to verify the solutions
by using mathematical software.

3. Assign students to attempt Exercise 8.12 in the Student’s Book.
Advise students to submit their work; check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 8.12

)
2
2
′
x
1. (a) f ′ () 2x = xe (b) ( )gx = e x ( 1 12x− − 6x
⎞
′
( ) e=
(c) hx x ⎛ ⎜ 1 + ln x (d) fx = x 3 9 ln9 9 3x+ x 2
⎟
1
x
( )
⎝ x ⎠
2. y′ = (cos x − sin 2 ) xe cosx 5. f ′ () 2x = xe + x e
2 x
x
2x
( )
2
6. (a) y′ = 4sin 8xe sin 4x (b) y′ = (2ln3 )3
x
2
(c) y′ = (1 x+ ln ) 3 3 (d) x′ = sec θ e tanθ
2
2
(e) x′ = 3t + 6te − 3t 2 + sec tant t (f) v′ = (2u + ) 2 e u + 2u− 8
x 3 ln 2x ⎡ 3 1 ⎤
10. y′ = ⎢ + −− ⎥
1 cot x
e x x ln 2x ⎦
161
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