What is the derivative of (2x-3)e^{3x} ?

The derivative of (2x-3)e^{3x} is 6e^{3x}x-7e^{3x}

What is the first derivative of (2x-3)e^{3x} ?

The first derivative of (2x-3)e^{3x} is 6e^{3x}x-7e^{3x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(2 x - 3) e^{3 x}

6 e^{3 x} x - 7 e^{3 x}

Solution steps

\frac{d}{d x} ((2 x - 3) e^{3 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x - 3, g = e^{3 x}

= \frac{d}{d x} (2 x - 3) e^{3 x} + \frac{d}{d x} (e^{3 x}) (2 x - 3)

\frac{d}{d x} (2 x - 3) = 2

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

Simplify

2 e^{3 x} + e^{3 x} \cdot 3 (2 x - 3) : 6 e^{3 x} x - 7 e^{3 x}

= 6 e^{3 x} x - 7 e^{3 x}

\int sec (a) x tan (a) x d x

\frac{d y}{d x} + 2 y = e^{3 x} y^{2}

\int \frac{1}{1 + 1 - x ^{2}} d x

\int \frac{1}{( x ^{2} + 1 ) ^{3}} d x

What is the derivative of (2x-3)e^{3x} ?
The derivative of (2x-3)e^{3x} is 6e^{3x}x-7e^{3x}
What is the first derivative of (2x-3)e^{3x} ?
The first derivative of (2x-3)e^{3x} is 6e^{3x}x-7e^{3x}