NCERT Solutions
Class 12 - Mathematics Part-1 - Chapter 5: CONTINUITY AND DIFFERENTIABILITYExercise 5.7
Class 12 - Mathematics Part-1 - Chapter 5: CONTINUITY AND DIFFERENTIABILITY
Question. 1
Find the second order derivative of the function \(y = x^2 + 3x + 2\).
Answer:
\(\dfrac{d^2y}{dx^2} = 2\)
Question. 2
Find the second order derivative of the function \(y = x^{20}\).
Answer:
\(\dfrac{d^2y}{dx^2} = 380x^{18}\)
Question. 3
Find the second order derivative of the function \(y = x\cdot \cos x\).
Answer:
\(\dfrac{d^2y}{dx^2} = -x\cos x - 2\sin x\)
Question. 4
Find the second order derivative of the function \(y = \log x\).
Answer:
\(\dfrac{d^2y}{dx^2} = -\dfrac{1}{x^2}\)
Question. 5
Find the second order derivative of the function \(y = x^3\log x\).
Answer:
\(\dfrac{d^2y}{dx^2} = x(5 + 6\log x)\)
Question. 6
Find the second order derivative of the function \(y = e^x\sin 5x\).
Answer:
\(\dfrac{d^2y}{dx^2} = 2e^x(5\cos 5x - 12\sin 5x)\)
Question. 7
Find the second order derivative of the function \(y = e^{6x}\cos 3x\).
Answer:
\(\dfrac{d^2y}{dx^2} = 9e^{6x}(3\cos 3x - 4\sin 3x)\)
Question. 8
Find the second order derivative of the function \(y = \tan^{-1}x\).
Answer:
\(\dfrac{d^2y}{dx^2} = -\dfrac{2x}{(1 + x^2)^2}\)
Question. 9
Find the second order derivative of the function \(y = \log(\log x)\).
Answer:
\(\dfrac{d^2y}{dx^2} = -\dfrac{1 + \log x}{(x\log x)^2}\)
Question. 10
Find the second order derivative of the function \(y = \sin(\log x)\).
Answer:
\(\dfrac{d^2y}{dx^2} = -\dfrac{\sin(\log x) + \cos(\log x)}{x^2}\)
Question. 12
If \(y = \cos^{-1}x\), find \(\dfrac{d^2y}{dx^2}\) in terms of \(y\) alone.
Answer:
\(\dfrac{d^2y}{dx^2} = -\cot y\,\cosec^2 y\)