Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

If x = 2at, y = at², where a is a constant, then find \[\frac{d^2 y}{d x^2} \text { at }x = \frac{1}{2}\] ?

If \[y = 1 - x + \frac{x^2}{2!} - \frac{x^3}{3!} + \frac{x^4}{4!}\] .....to ∞, then write  \[\frac{d^2 y}{d x^2}\] in terms of y ?

If y = x + e^x, find \[\frac{d^2 x}{d y^2}\] ?

If y = |x − x²|, then find \[\frac{d^2 y}{d x^2}\] ?

If x = f(t) and y = g(t), then write the value of \[\frac{d^2 y}{d x^2}\] ?

If \[y = \left| \log_e x \right|\] find\[\frac{d^2 y}{d x^2}\] ?

If x = a cos nt − b sin nt, then \[\frac{d^2 x}{d t^2}\] is 

If x = at², y = 2 at, then \[\frac{d^2 y}{d x^2} =\] 

If y = axⁿ⁺¹ + bx⁻ⁿ, then \[x^2 \frac{d^2 y}{d x^2} =\] 

\[\frac{d^{20}}{d x^{20}} \left( 2 \cos x \cos 3 x \right) =\]

If x = t², y = t³, then \[\frac{d^2 y}{d x^2} =\] 

If y = a + bx², a, b arbitrary constants, then

If f(x) = (cos x + i sin x) (cos 2x + i sin 2x) (cos 3x + i sin 3x) ...... (cos nx + i sin nx) and f(1) = 1, then f'' (1) is equal to

If y = a sin mx + b cos mx, then \[\frac{d^2 y}{d x^2}\]   is equal to

If \[f\left( x \right) = \frac{\sin^{- 1} x}{\sqrt{1 - x^2}}\] then (1 − x)² f '' (x) − xf(x) =

If \[y = \tan^{- 1} \left\{ \frac{\log_e \left( e/ x^2 \right)}{\log_e \left( e x^2 \right)} \right\} + \tan^{- 1} \left( \frac{3 + 2 \log_e x}{1 - 6 \log_e x} \right)\], then \[\frac{d^2 y}{d x^2} =\]

Let f(x) be a polynomial. Then, the second order derivative of f(e^x) is

If y = a cos (log_e x) + b sin (log_e x), then x² y₂ + xy₁ =

If x = 2 at, y = at², where a is a constant, then \[\frac{d^2 y}{d x^2} \text { at x } = \frac{1}{2}\] is 

If x = f(t) and y = g(t), then \[\frac{d^2 y}{d x^2}\] is equal to