Question

if y=I n (In x) , then dy/dx is equal to....

Plz answer​

Answer 1

Answer:

option a is correct

Explanation:

☆derivative of lnx=1/x

☆for complex, we need to do double integrtion

dy/dx= d/dx(ln(lnx))

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^

treat as x'

= d/dx(lnx').d/dx(x')

=1/lnx.1/x where x' is lnx

=1/xlnx

Answer 2

$\sf \rightarrow \quad y = ln(ln \: x) \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{d}{dx} \bigg( ln(ln \: x)\bigg) \\ \\ \sf \: \: Applying \: chain \: rule \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{d(ln(ln \: x))}{d ( ln \: x)} \cdot \frac{d (ln \: x)}{dx} \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{ln \: x} \cdot \frac{1}{x} \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{ x \: ln \: x} \\ \\ \\ \underline{ \sf Properties \: Used} \\ \\ \qquad \sf \hookrightarrow \frac{d( \blue{ln \: } \red{x})}{d \red{x}} = \frac{1}{ \red{x}} \\ \\ \sf \qquad \hookrightarrow \: Chain \: rule \\ \qquad \quad \sf \frac{d \green{y}}{ d \red{x}} = \frac{d \green{y}}{d \blue{u}} \cdot \frac{d \blue{u}}{d \red{x}}$