If y = ₂026}(₂025} x), then dy/dx =

Correct Answer is : 1xlog⁡xlog⁡20261/x x 2026xlogxlog20261

Correct Answer is : 1xlog⁡xlog⁡20261/x x 2026xlogxlog20261

Test Index

GUJCET 2026 Math Paper

Question : 18 of 40

Marks: +1, -0

y = \log_{2026}(\log_{2025} x)

\frac{dy}{dx} = \dots \dots \dots

Solution:

Concept:

Differentiate a composition of logarithms using the chain rule and change of base.

Explanation:

Let

u=\log_{2025}x=\frac{\log x}{\log 2025}

Then

y=\log_{2026}u=\frac{\log u}{\log 2026}

By the chain rule,

\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}

Now

\frac{dy}{du}=\frac{1}{u\log 2026}

Also

\frac{du}{dx}=\frac{1}{x\log 2025}

\frac{dy}{dx}=\frac{1}{u\log 2026}\cdot\frac{1}{x\log 2025}

Substitute

u=\frac{\log x}{\log 2025}

\frac{dy}{dx}=\frac{1}{\left(\frac{\log x}{\log 2025}\right)\log 2026\cdot x\log 2025}

Simplify to get

\frac{dy}{dx}=\frac{1}{x\log x\log 2026}

Answer:

Option (C):

\frac{1}{x\log x\log 2026}

Go to Question:

Prev Question

Next Question