Chapter 1 Differentiation Miscellaneous Exercise 1

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Chapter 1 Differentiation Miscellaneous Exercise 1

Chapter 1 Differentiation Miscellaneous Exercise 1

(I) Choose the correct option from the given alternatives:

Question 2.

Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 I Q2

Question 3.

Question 4.

Question 5.

Question 6.


Question 7.
If y is a function of x and log(x + y) = 2xy, then the value of y'(0) = _______

(a) 2
(b) 0
(c) -1
(d) 1
Answer:
(d) 1

Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 I Q7.1

Question 8.

Question 9.

Question 10.

Question 11.


Question 12.

(II) Solve the following:

Question 1.


Let u(x) = f[g(x)], v(x) = g[f(x)] and w(x) = g[g(x)]. Find each derivative at x = 1, if it exists i.e. find u'(1), v'(1) and w'(1). if it doesn’t exist then explain why?
Solution:




Question 2.
The values of f(x), g(x), f'(x) and g'(x) are given in the following table:
Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 II Q2
Match the following:

Solution:


Question 3.
Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1.


Solution:




Question 4.


Solution:


Solution:



Solution:


Question 5.

Differentiating both sides w.r.t. x, we get


Differentiating both sides w.r.t. x, we get


Solution:

x sin(a + y) + sin a . cos (a + y) = 0 ….. (1)
Differentiating w.r.t. x, we get



Solution:
Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 II Q5 (iv)

Question 6.

Solution:

Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 II Q6 (i)
Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 II Q6 (i).1
Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 II Q6 (i).2
Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 II Q6 (i).3
Maharashtra Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1 II Q6 (i).4


Solution:



Solution:


Question 7.

Differentiating both sides w.r.t. x, we get



Solution:


Solution:

x = a cos θ, y = b sin θ
Differentiating x and y w.r.t. θ, we get

(iv) If y = A cos(log x) + B sin(log x), show that  + y = o.
Solution:
y = A cos (log x) + B sin (log x) …… (1)

Differentiating both sides w.r.t. x, we get


Differentiating w.r.t. x, we get