Question

derivative of y=ae^x​

Answer 1

Answer:

The answer is ae^x

Explanation:

y=ae^x

Differentiating both sides with respect to x

dy/dx

= d/dx (ae^x)

= a × d/dx (e^x)

= ae^x

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Answer 2

GIVEN :–

• A function $\: \: { \bold{y = a {e}^{x} }}$

TO FIND :–

$\\ \: \: { \huge{.}} \: \: { \bold{ \dfrac{dy}{dx}=?}}$

SOLUTION :–

$\\ \implies{ \bold{y = a {e}^{x} }}$

• Differentiate with respect to 'x' –

$\\ \implies{ \bold{ \dfrac{dy}{dx} = \dfrac{d(a {e}^{x})}{dx}}}$

• Using property –

$\\ \dashrightarrow \: { \bold{ \dfrac{d \{k.f(x) \}}{dx} = k. \dfrac{d \{f(x) \}}{dx}}}$

$\\ \implies{ \bold{ \dfrac{dy}{dx} = a. \dfrac{d( {e}^{x})}{dx}}}$

• Using property –

$\\ \dashrightarrow \: { \bold{ \dfrac{d ( {e}^{x} )}{dx} = {e}^{x} }}$

• So that –

$\\ \implies \large{ \boxed{ \bold{ \dfrac{dy}{dx} = a {e}^{x}}}}$