GUJCET 2025 Math Paper

Question : 20 of 40

Marks: +1, -0

\frac{d}{dx}(5^{\log x}) = \dots

Solution:

Concept:

Differentiate an exponential function with a variable exponent by rewriting it as a power of

x

Explanation:

Let

y = 5^{\log x}

Using the identity

a^{\log_{10} b} = b^{\log_{10} a}

, we get

y = x^{\log 5}

Differentiate using the power rule

\frac{d}{dx}(x^n) = n x^{n-1}

Here

n = \log 5

So,

\frac{dy}{dx} = (\log 5) \cdot x^{\log 5 - 1}

This matches option C.

Answer:

\frac{dy}{dx} = \log 5 \cdot x^{\log 5 - 1}

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