Question

Which of the following is derivative of \(\sqrt{a^{\sqrt{x}}}\) with respect to \(x\)?

• A. \(\dfrac{\sqrt{a^{\sqrt{x}}}}{2\sqrt{x}}\)
• B. \(\dfrac{\sqrt{a^{\sqrt{x}}}\log_e a}{2\sqrt{x}}\)
• C. \(\dfrac{a^{\sqrt{x}}\sqrt{a^{\sqrt{x}}}\log_e a}{2\sqrt{x}}\)
• D. \(\dfrac{\sqrt{a^{\sqrt{x}}}}{4\sqrt{x}\log_a e}\)

Hint:

First convert \(\sqrt{a^{\sqrt{x}}}\) into \(a^{\frac{\sqrt{x}}{2}}\), then apply the differentiation formula of \(a^{f(x)}\).

Answer 1

The Correct Option is D