Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Find the derivatives of the following functions with respect to corresponding independent variables:

Question 1.
f(x) = x – 3 sin x
Answer:
f(x) = x – 3 sin x
f'(x) = 1 – 3 cos x

Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Question 2.
y = sin x + cos x
Answer:
y = sin x + cos x
\(\frac{d y}{d x}\) = cos x – sin x

Question 3.
f(x) = x sin x
Answer:
f(x) = x sin x
f'(x) = x cos x + sin x – 1
f'(x) = x cos x + sin x

Question 4.
y = cos x – 2 tan x
Answer:
y = cos x – 2 tan x
\(\frac{d y}{d x}\) = – sin x – 2 sec2 x

Question 5.
g(t) = t3 cos t
Answer:
g(t) = t3 cos t
g'(t) = t3 × – sin t + cos t × 3t2
g'(t) = – t3 sin t + 3t2 cos t
= 3t2 cos t – t3 sin t

Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Question 6.
g(t) = 4 sec t + tan t
Answer:
g(t) = 4 sec t + tan t
g'(t) = 4 sec t tan t + sec2t

Question 7.
y = ex sin x
Answer:
y = ex sin x
\(\frac{d y}{d x}\) = ex cos x + sin x ex
\(\frac{d y}{d x}\) = ex (sin x + cos x)

Question 8.
y = \(\frac{\tan x}{x}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 1

Question 9.
y = \(\frac{\sin x}{1+\cos x}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 2

Question 10.
y = \(\frac{x}{\sin x+\cos x}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 3

Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Question 11.
y = \(\frac{\tan x-1}{\sec x}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 4
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 5

Question 12.
y = \(\frac{\sin x}{x^{2}}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 6

Question 13.
y = tan θ (sin θ + cos θ)
Answer:
y = tan θ (sin θ + cos θ)
\(\frac{d y}{d x}\) = tan θ (cos θ – sin θ) + (sin θ + cos 0) sec2 θ
= tan θ cos θ – tan θ sin θ + sin θ sec2θ + cos θ sec2θ
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 7
= sin θ – sin2θ sec θ + tan θ sec θ + sec θ
= sin θ + (1 – sin2θ) sec θ + sec θ tan θ
= sin θ + cos2θ × \(\frac{1}{\cos \theta}\) + sec θ tan θ
= sin θ + cos θ + sec θ tan θ

Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Question 14.
y = cosec x . cot x
Answer:
y = cosec x . cot x
\(\frac{d y}{d x}\) = cosec x × – cosec2 x + cot x × – cosec x cot x
= – cosec3 x – cosec x cot2 x
= – cosec x (cosec2 x + cot2 x)
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 8

Question 15.
y = x sin x cos x
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 9

Question 16.
y = e-x . log x
Answer:
y = e-x . log x
\(\frac{d y}{d x}\) = e-x × \(\frac{1}{x}\) + (log x) e-x (-1)
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 10

Question 17.
y = (x2 + 5) log (1 + x) e-3x
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 11

Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Question 18.
y = sin x0
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 12

Question 19.
y = log10 x
Answer:
y = log10 x
y = logex . log10e
Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 13

Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2

Question 20.
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Answer:
f(x) = 2x2 – 5x + 3
f'(x) = 4x – 5
x = 0, f'(0) = 4 × 0 – 5 = – 5
x = 1, f'(0) = 4 × 1 – 5 = – 1
x = 2, f'(0) = 4 × 2 – 5 = – 3

Samacheer Kalvi 11th Maths Guide Chapter 10 Differentiability and Methods of Differentiation Ex 10.2 16

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