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NCERT Class 12 Maths Chapter 5: Continuity And Differentiability 17 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 5 Continuity And Differentiability — Exercise 5.7

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Find the second derivative of \(x^{2} + 3 x + 2\) with respect to x; on R.

Find the second derivative of \(x^{20}\) with respect to x; on R.

Find the second derivative of \(x \cos{\left(x \right)}\) with respect to x; on R.

Find the second derivative of \(\log{\left(x \right)}\) with respect to x; for x>0.

Find the second derivative of \(x^{3} \log{\left(x \right)}\) with respect to x; for x>0.

Find the second derivative of \(e^{x} \sin{\left(5 x \right)}\) with respect to x; on R.

Find the second derivative of \(e^{6 x} \cos{\left(3 x \right)}\) with respect to x; on R.

Find the second derivative of \(\operatorname{atan}{\left(x \right)}\) with respect to x; on R.

Find the second derivative of \(\log{\left(\log{\left(x \right)} \right)}\) with respect to x; for x>1.

Find the second derivative of \(\sin{\left(\log{\left(x \right)} \right)}\) with respect to x; for x>0.

If y=5cos x−3sin x, prove y″+y=0.

For y=cos⁻¹x, express y″ in terms of y alone.

If y=\(4 \sin{\left(\log{\left(x \right)} \right)} + 3 \cos{\left(\log{\left(x \right)} \right)}\), show x²y″+xy′+y=0.

If y=\(A e^{m x} + B e^{n x}\), show y″−(m+n)y′+mny=0.

If y=\(500 e^{7 x} + 600 e^{- 7 x}\), show y″=49y.

If eʸ(x+1)=1, prove y″=(y′)².

If y=\(\operatorname{atan}^{2}{\left(x \right)}\), show (x²+1)²y″+2x(x²+1)y′=2.