NCERT Solutions For Class 12 Maths Chapter 5 Continuity and Differentiability Exercise Miscellaneous Question 1 to 23 Answer: Downlaod pdf

Differentiate w.r.t. x the function in Exercises 1 to 11

Question 1:(3x2 – 9x + 5)9

Question 2:sin3 x + cos6 x

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Question 3:(5x)3 cos 2x

exercise Miscellaneous maths class 12 Chapter 5 Continuity and Differentiability

Question 4:sin–1(x x ), 0 ≤ x ≤ 1

Question 5: 1 cos 2 2 7 x x − + , – 2 < x < 2

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Question 6: 1 1 sin 1 sin cot 1 sin 1 sin x x x x − + + −    + − −  , 0 < x < 2 p

Question 7:(log x)log x, x > 1

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Question 8:cos (a cos x + b sin x), for some constant a and b.

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Question 9:(sin x – cos x) (sin x – cos x), 3 4 4 x π p < <

Question 10:xx + xa + ax + aa, for some fixed a > 0 and x > 0

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Question 11:( ) 2 2 3 3 x x x x − + − , for x > 3

Question 12:Find dy dx , if y = 12 (1 – cos t), x = 10 (t – sin t), 2 2 t π p − < <

Question 13:Find dy dx , if y = sin–1 x + sin–1 2 1− x , 0 < x < 1

Exercise Miscellaneous class 12 Math ncert solutions Chapter 5

Question 14:If x 1+ y + y 1+ x = 0 , for , – 1 < x < 1, prove that ( )2 1 1 dy dx x = − +

Question 15:If (x – a)2 + (y – b)2 = c2, for some c > 0, prove that 3 2 2 2 2 1 dy dx d y dx    +      is a constant independent of a and b.

Differentiate w.r.t. x the function in Exercises 1

Question 16:If cos y = x cos (a + y), with cos a ¹ ± 1, prove that 2 cos ( ) sin dy a y dx a + = .

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Question 17:If x = a (cos t + t sin t) and y = a (sin t – t cos t), find 2 2 d y dx .

Question 18:If f (x) = | x |3, show that f ²(x) exists for all real x and find it.

Continuity and Differentiability Math ncert solution class 12

Question 19:Using mathematical induction prove that ( n ) n 1 d x nx dx − = for all positive integers n.

Question 20:Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.

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Question 21:Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

CBSE NCERT Solutions For Class 12 Continuity and Differentiability

Question 22:If f (x) g(x) h(x) y l m n a b c = , prove that f (x) g (x) h (x) dy l m n dx a b c ¢ ¢ ¢ =

Question 23:If y = 1 a cos x e − , – 1 ≤ x ≤ 1, show that ( ) 2 2 2 2 1 0 d y dy x x a y dx dx − − − = .

Ncert Solution for class 6 to 12 download in pdf

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