Ms. Remka of city school is teaching chain rule to  her students with the help of a flow-chart  The chain rule says that if h and g are functions and  f ( x ) = g(h(x )), then

Based on the above information, answer any four  of the following questions. 
Let f(x) = sin x and g(x) = x3

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Question 1

fog (x) =  _______.

(a) sin x3  

(b) sin3 x

(c) sin 3x  

(d) 3 sin x

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Question 2

gof (x) =  _______.

(a) sin x3  

(b) sin3 x

(c) sin 3x 

(d) 3 sin x

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Question 3

d / dx (sin3 x) =  _______.

(a) cos3 x 

(b) 3 sinx cos x

(c) 3 sin2x cos x  

(d) −cos3 x

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Question 4

d / dx ( sin x3) _______.

(a) cos (x)3  

(b) −cos (x)3

(c) 3x2 sin (x)3  

(d) 3x2 cos (x3)

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Question 5

d / dx (sin 2x) at x = π/2 is _______.

(a) 0 

(b) 1

(c) 2 

(d) −2

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Transcript

Question Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if h and g are functions and f(x) = g(h(x)), then Based on the above information, answer any four of the following questions. Let f(x) = sin x and g(x) = x3 Question 1 fog (x) = _______. (a) sin x3 (b) sin3 x (c) sin 3x (d) 3 sin x Since f(x) = sin x and g(x) = x3 fog (x) = f(g(x)) = f (x3) = sin (x3) So, the correct answer is (A) Question 2 gof (x) = _______. (a) sin x3 (b) sin3 x (c) sin 3x (d) 3 sin x Since f(x) = sin x and g(x) = x3 gof (x) = g(f(x)) = g(sin x) = (sin x)3 = sin3 x So, the correct answer is (B) Question 3 𝒅/𝒅𝒙 (sin3 x) = _______. (a) cos3 x (b) 3 sinx cos x (c) 3 sin2x cos x (d) −cos3 x (sin3 x)’ = 3 sin2 x (sin x)’ = 3 sin2 x cos x So, the correct answer is (C) Question 4 𝒅/𝒅𝒙 (sin x3) _______. (a) cos (x)3 (b) −cos (x)3 (c) 3x2 sin (x)3 (d) 3x2 cos (x3) [sin (x3)]’ = cos (x3) × (x3)’ = cos (x3) × 3x2 = 3x2 cos (x3) So, the correct answer is (D) Question 5 𝒅/𝒅𝒙 (sin 2x) at x = 𝜋/2 is _______. (a) 0 (b) 1 (c) 2 (d) −2 𝒅/𝒅𝒙 (sin 2x) = 2 cos 2x Putting x = 𝜋/2 = 2 cos (2 × 𝜋/2) = 2 cos 𝜋 = 2 × −1 = −2 So, the correct answer is (D)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.