Question

pls ans fast. multiple correct. For which functions dy/dx = d^2y/dx^2.
does not hold true?
A) sinx = y B) e^x = y. C) cosx = y. D) x^2 = y​

Answer 1

Answer:

ans d

• double differentiation of x 2 is only a constant and never can be a variable

Answer 2

Answer:

A)y=Sinx ;C)y=Cosx and D)$y=x^{2}$

Step-by-step explanation:

In this question,

We have to verify for which functions

$\frac{\mathrm{d} y}{\mathrm{d} x}\neq\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}$ does not holds true.

A)y=Sinx

$\frac{\mathrm{d} y}{\mathrm{d} x}=Cosx$

$\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}=-Sinx$

Hence,$\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}$

B)y$=e^{x}$

$\frac{\mathrm{d} y}{\mathrm{d} x}=e^{x}$

$\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}=e^{x}$

Hence,$\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}$

C)y=Cosx

$\frac{\mathrm{d} y}{\mathrm{d} x}=-Sinx$

$\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}=-Cosx$

Hence,$\frac{\mathrm{d} y}{\mathrm{d} x}\neq\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}$

D)y$=x^{2}$

$\frac{\mathrm{d} y}{\mathrm{d} x}=2x$

$\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}=2$

Hence,$\frac{\mathrm{d} y}{\mathrm{d} x}\neq\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}$

Therefore For y=Cosx;y=Sinx and y$=x^{2}$

$\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}$ does not holds true.