Chapter 1 Differentiation Miscellaneous Exercise 1 Solutions

Balbharti12th Maharashtra State Board Maths Solutions BookPdf Chapter 1 Differentiation Miscellaneous Exercise 1 Questions and Answers.

Maharashtra State Board 12th Maths Solutions Chapter 1 Differentiation Miscellaneous Exercise 1

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

(II) Solve the following:

(ii)
Solution:
Let y =
Put x = cos θ. Then θ = cos^-1x and

(iii)
Solution:

(iv)
Solution:
Let y =
Put x = cos θ. Then θ = cos^-1x and

(v)
Solution:

(vi)
Solution:

(ii) If , then show that
Solution:


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

(iii) If x sin(a + y) + sin a cos(a + y) = 0, then show
Solution:
x sin(a + y) + sin a. cos (a + y) = 0 ….. (1)
Differentiating w.r.t. x, we get

(iv) If sin y = x sin(a + y), then show that
Solution:

(v) If x = , then show that
Solution:
x =
= log x …..(1)
y =

(vi) If y = f(x) is a differentiable function of x, then show that
Solution:
If y = f(x) is a differentiable function of x such that inverse function x = f^-1(y) exists,

(ii) Differentiate w.r.t. cos(log x)
Solution:

(iii) Differentiate w.r.t.
Solution:

(ii) If log y = log(sin x) – x², show that
Solution:

(iii) If x = a cos θ, y = b sin θ, show that
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 x²y₂+ xy₁+ y = o.
Solution:
y = A cos (log x) + B sin (log x) …… (1)
Differentiating both sides w.r.t. x, we get

(v) If y = A e^mx+ B e^nx, show that y₂– (m + n) y₁+ (mn) y = 0.
Solution:
y = A e^mx+ B e^nx
Differentiating w.r.t. x, we get