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Continuity and Differentiability EXERCISE 5.7 Solutions
- Q1: Find the second order derivatives of the functions $x^2 + 3x + 2$
- Q2: Find the second order derivatives of the functions $x^{20}$
- Q3: Find the second order derivatives of the functions $x \cdot \cos x$
- Q4: Find the second order derivatives of the functions $\log x$
- Q5: Find the second order derivatives of the functions. $x^3 \log x$
- Q6: Find the second order derivatives of the functions. $e^x \sin 5x$
- Q7: Find the second order derivatives of the functions. $e^{6x} \cos 3x$
- Q8: Find the second order derivatives of the functions. $\tan^{-1} x$
- Q9: Find the second order derivatives of the functions. $\log(\log x)$
- Q10: Find the second order derivatives of the functions. $\sin(\log x)$
- Q11: If $y = 5 \cos x - 3 \sin x$, prove that $\frac{d^2y}{dx^2} + y = 0$
- Q12: If $y = \cos^{-1} x$, Find $\frac{d^2y}{dx^2}$ in terms of $y$ alone.
- Q13: If $y = 3 \cos(\log x) + 4 \sin(\log x)$, show that $x^2 y_2 + xy_1 + y = 0$
- Q14: If $y = Ae^{mx} + Be^{nx}$, show that $\frac{d^2y}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0$
- Q15: If $y = 500e^{7x} + 600e^{-7x}$, show that $\frac{d^2y}{dx^2} = 49y$
- Q16: If $e^y (x + 1) = 1$, show that $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$
- Q17: If $y = (\tan^{-1} x)^2$, show that $(x^2 + 1)^2 y_2 + 2x(x^2 + 1)y_1 = 2$
Other Exercises for CBSE - Class 12 Mathematics Continuity and Differentiability
- Continuity and Differentiability Class 12 EXERCISE 5.1
- Continuity and Differentiability Class 12 EXERCISE 5.2
- Continuity and Differentiability Class 12 EXERCISE 5.3
- Continuity and Differentiability Class 12 EXERCISE 5.4
- Continuity and Differentiability Class 12 EXERCISE 5.5
- Continuity and Differentiability Class 12 EXERCISE 5.6
Chapters in CBSE - Class 12 Mathematics
Top Tutors who teach Continuity and Differentiability
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Online Classes 
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Maam is good and was able to resolve my queries. She is very calm explains the chapter thoroughly. It was just one class with her but we are going to have more in up coming days.
Top Tutor Adavikamalapur, Bhupalapalli Less than a yr Exp 2 students 75 hrs of classes completed 300 per hour Online Classes Iam Masters passed out student in biochemistry from central university of Rajasthan. I have interest towards make students understand and learn interesting stuff in science
Top Tutor Jhunjhunu Bypass Rd, Sikar 5 yrs of Exp 4 students 10 hrs of classes completed 150 per hour Online Classes Tutor's home I have over 5 years of teaching experience in Class 12th Biology and chemistry as well, helping students build a strong foundation for both board exams and NEET preparation. My teaching method is concept-driven, where I explain each topic with clarity, real-life examples, and visual representation using a whiteboard setup, creating a true classroom-like environment. I cover the full Class 12 CBSE syllabus, including all core chapters such as: Reproduction (Human and Plants) Genetics and Evolution Biotechnology Human Health and Disease Ecology and Environment I focus on: NCERT line-by-line explanation Diagram-based questions Important previous year board and NEET questions Tips for writing high-scoring answers in board exams Clarifying complex concepts with simple analogies Many of my students have improved significantly in both their conceptual understanding and exam performance, and some have even scored above 90% in boards and qualified for NEET. My aim is to make Biology interesting and scoring — not just something to memorize, but something to truly understand.
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Top Tutor Patel Nagar, Gurgaon 7 yrs of Exp 550 per hour Online Classes 
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