GATE 2020 MT – Question 27

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple choice

For $y=a^x$, find dy/dx at x = 1.

Show answer and explanation

Correct answer: (D) $a\ln a$

Explanation

Write $a^x=e^{x\ln a}$ for the usual real domain a > 0. Differentiation gives $dy/dx=a^x\ln a$. At x = 1 this is $a\ln a$, D.

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