Math, asked by dkkddk, 4 months ago

plz help me......... ​

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Answered by BrainlyEmpire
53

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}}}} \\

Answered by Anonymous
16

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}}}} \\

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