Question

derivative of (a^x/Log a)?

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Answer 1

To differentiate :-

$\sf{\dfrac{a^x}{log(a)} }$

OR

$\sf{\dfrac{a^x}{ln(a)} }$

Solution :-

$\sf{Let\ y=\dfrac{a^x}{ln(a)} }$

$\sf{=\dfrac{d}{dx}\bigg[\dfrac{a^x}{ln(a)} \bigg] }$

(Linear differentiation)

$\sf{=\dfrac{1}{ln(a)}.\dfrac{d}{dx}(a^x) }$

$\sf{=\dfrac{ln(a)a^x}{ln(a)} }$

$\boxed{\sf{=a^x}}$

Applied :-

◘ Linear differentiation

→ $\sf{[a.b(x)+c.d(x)]'=a.b'(x)+c.d'(x)}$

◘ Exponential function rule

→ $\sf{(a^x)'=ln(a).a^x}$