Question

If y=logx then d²y/dx² is equal to

Answer 1

Answer:

$\frac{-1}{x^{2} }$

Step-by-step explanation:

d²y/dx² is nothing but differentiating the equation two times

or it can be considered as:

$\frac{d}{dx} *\frac{dy}{dx}$

therefore,

$\frac{dy}{dx} = \frac{d(logx)}{dx} = \frac{1}{x}$     ........(simple differentiation)

now, on the second part:

$\frac{d}{dx}$ of $\frac{1}{x}$

 i.e. $\frac{d(x^{-1} )}{dx} = -1 x^{-2} =\frac{-1}{x^{2} }$

[here's a short trick for differentiation of reciprocals:

 for e.g. $\frac{1}{x^{2} }$

 ---> see the power of "x" and make it negative

         in this case its -2

 ---> Make it as the numerator and increase the power of "x" by 1

        therefore $\frac{-2}{x^{3} }$

you can check it by doing simple differentiation ]