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Mathematics 1A Tutorial
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- Mathematics 1A (EN1911)
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- The Robert Gordon University (RGU)
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Rules of Differentiation Tutorial EN1911 (Mathematics 1A) 1Tutorial Questions on Rules of Differentiation
A: Chain Rule
1. Differentiate the following functions with respect to x.
1
(a) (𝑥 + 2)2 (b) (𝑥−3)2 (c) sin(𝑥 + 1) (d) cos(2𝑥)
(e) (2𝑥 + 3)4 (f) sin(3𝑥 − 5) (g) exp(4 − 2𝑥) (h) ln(3𝑥 + 2)
2. Differentiate the following functions with respect to x.
(a) √1 − 𝑥 2 (b) sin(3𝑥 3 ) (c) ln(cos(𝑥))
(d) exp(ln(𝑥)) (e) cos 2 (𝑥)
3. Differentiate the following functions with respect to x.
(a) ln(sin(2𝑥 + 3)) (b) exp(− cos 2 (𝑥)) (c) (ln(𝑥 + 3))5
B: Product Rule
4. Differentiate the following functions with respect to x:
(a) 𝑥 2 ln(𝑥) (b) 𝑒 𝑥 sin(𝑥) (c) √𝑥cos(𝑥) (d) (𝑥 3 − 𝑥 + 4)𝑒 𝑥
5. Differentiate the following functions with respect to x:
(a) 𝑒 3𝑥 sin(2𝑥) (b) (√𝑥 2 + 1)cos(𝑥) (c) 𝑥 3 sin(𝑥) ln(𝑥)
6. Differentiate the following functions with respect to x:
(a) 𝑥 5 sin(𝑥) (b) 𝑒 𝑥 cos(𝑥) (c) 𝑥 3 tan(𝑥)
7. Differentiate the following functions with respect to x:
(a) 𝑥 4 cos(𝑥) (b) 5 𝑥 2 sin(𝑥) (c) 2𝑒 𝑥 ln(𝑥)
C: Quotient Rule
8. Differentiate the following quotients with respect to x:
𝑥3 𝑒 −2𝑥 ln(𝑥)
(a) cos(𝑥) (b) (c)
𝑥 2 +1 sin(2𝑥−5)
9. Differentiate the following quotients with respect to x:
cos(𝑥) 3𝑥 2 log(𝑥)
(a) (b) (c)
sin(𝑥) cos(𝑥) 𝑥3
10. Differentiate the following quotients with respect to x:
cos(𝑥) sin(𝑥) cos(𝑥)
(a) 𝑥 3 (b) 2𝑒 𝑥 (c) tan(𝑥)
D: Mixture of Rules
11. Differentiate the following with respect to x:
(2𝑥−3)3 ln(3𝑥 2 )
(a) (b)
𝑒 3𝑥+2 sin(2𝑥−3)
12. Differentiate with respect to x, using the appropriate rule(s):
𝑒 −𝑥
(a) (𝑥 3 + 𝑥) sin(𝑥) (b) (c) cos(ln(𝑥)) (d) 𝑥 2 sin(3𝑥 2 )
2𝑥+3
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