Question

if y = | logex| , find d^2 y/dx^2​

Answer 1

Answer:

y=log(logx)

Again differentiate both sides w.r.t. x

dx

dy

=

logx

1

dx

d

(logx)

dx

dy

=

logx

1

×

x

1

×1

dx

dy

=

xlogx

1

Again differentiate both sides w.r.t. x

dx

2

d

2

y

=

(xlogx)

2

xlogx(0)−1[logx+x×

x

1

]

dx

2

d

2

y

=

(xlogx)

2

−(1+logx)

Answer 2

Answer:

Answer is (-1) /x^2

Step-by-step explanation:

dy/dx = 1/x

d^2y/dx^2 = [x * d(1) - 1 * d(x) ] / x^2 = [x * 0 - 1 * 1] / x^2

= -1/(x^2)