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Free CBSE - Class 12 Mathematics - Continuity and Differentiability worksheets

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1.
If $y = Ae^{mx} + Be^{nx}$, show that $\frac{d^2y}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0$
2.
If $y = 500e^{7x} + 600e^{-7x}$, show that $\frac{d^2y}{dx^2} = 49y$
3.
If $e^y (x + 1) = 1$, show that $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$
4.
If $y = (\tan^{-1} x)^2$, show that $(x^2 + 1)^2 y_2 + 2x(x^2 + 1)y_1 = 2$
5.

Find the second order derivatives of the functions. $\tan^{-1} x$

6.

Find the second order derivatives of the functions. $\log(\log x)$

7.

Find the second order derivatives of the functions. $\sin(\log x)$

8.
If $y = 5 \cos x - 3 \sin x$, prove that $\frac{d^2y}{dx^2} + y = 0$
9.
If $y = \cos^{-1} x$, Find $\frac{d^2y}{dx^2}$ in terms of $y$ alone.
10.
If $y = 3 \cos(\log x) + 4 \sin(\log x)$, show that $x^2 y_2 + xy_1 + y = 0$
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