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# NCERT Solutions Class 12 Maths Continuity and Differentiability

Hi Students, Welcome to **Amans Maths Blogs (AMB)**. In this post, you will get the * NCERT Solutions for Class 12 Maths Continuity and Differentiability Miscellaneous Exercise*.

* CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise. This*

**CBSE NCERT Solutions for Class 12**^{th}Maths**can be downloaded in PDF file. The downloading link is given at last.**

*NCERT Solutions** NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**## NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise

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

**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 1.**

(3x^{2} – 9x + 5)^{9}

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 2.**

sin^{3} x + cos^{6} x

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 3.**

(5x)^{3 cos 2x}

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 4.**

sin^{–1}(x√x), 0 ≤ x ≤ 1

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 5.**

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 6.**

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 7.**

(log x)^{log x}, x > 1

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 8.**

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

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 9.**

(sin x – cos x)^{(sin x – cos x)}, π/4 < x < 3π/4

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 10.**

x^{x} + x^{a} + a^{x} + a^{a}, for some fixed a > 0 and x > 0

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 11.**

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 12.**

Find dy/dx, if y = 12 (1 – cos t), x = 10 (t – sin t), -π/2 < t < π/2.

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 13.**

Find dy/dx, if y = sin^{–1} x + sin^{–1 }√(1 – x2), -1 ≤ x ≤ 1.

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 14.**

If x√(1 + y) + y√(1 + x) = 0, for -1 < x < 1, prove that dy/dx = -1/(1 + x)^{2}.

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 15.**

If (x – a)^{2} + (y – b)^{2} = c^{2}, for some c > 0, prove that is a constant independent of a and b.

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 16.**

If cos y = x cos (a + y), with cos a ≠ ± 1, prove that .

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 17.**

If x = a (cos t + t sin t) and y = a (sin t – t cos t), find d^{2}y/dx^{2}.

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 18.**

If f (x) = | x |^{3}, show that f ″(x) exists for all real x and find it.

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 19.**

Using mathematical induction prove that for all positive integers n.

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 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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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 21.**

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

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 22.**

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**NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous ****Exercise****: Ques No 23.**

If – 1 ≤ x ≤ 1, show that .

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