What is the derivative of e 2 + 2 x e 3 + 4 x ?

Cancel the common factor of&nbsp;e2+2x&nbsp;and&nbsp;e3+4x.ddx[e2+2x-(3+4x)]Differentiate using the chain rule, which states that&nbsp;ddx[f(g(x))]&nbsp;is&nbsp;f′(g(x))g′(x)&nbsp;where&nbsp;f(x)=ex&nbsp;and&nbsp;g(x)=2+2x-(3+4x).e2+2x-(3+4x)ddx[2+2x-(3+4x)]Differentiate.-2⋅e2+2x-(3+4x)Simplify.-2e-2x-1

Resolved: "What is the derivative of e 2 +..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Carley Haley

Answered question

2022-05-12

What is the derivative of

\frac{e^{2 + 2 x}}{e^{3 + 4 x}}

Answer & Explanation

Kosyging1j7u

Beginner2022-05-13Added 16 answers

Cancel the common factor of $e^{2 + 2 x}$ and $e^{3 + 4 x}$ .

$\frac{d}{d x} [e^{2 + 2 x - (3 + 4 x)}]$

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = e^{x}$ and $g (x) = 2 + 2 x - (3 + 4 x)$ .

$e^{2 + 2 x - (3 + 4 x)} \frac{d}{d x} [2 + 2 x - (3 + 4 x)]$

Differentiate.

$- 2 \cdot e^{2 + 2 x - (3 + 4 x)}$

Simplify.

$- 2 e^{- 2 x - 1}$

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