What is the derivative of f(x)=3x^5e^{2x} ?

The derivative of f(x)=3x^5e^{2x} is 3(5x^4e^{2x}+e^{2x}*2x^5)

What is the first derivative of f(x)=3x^5e^{2x} ?

The first derivative of f(x)=3x^5e^{2x} is 3(5x^4e^{2x}+e^{2x}*2x^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = 3 x^{5} e^{2 x}

3 (5 x^{4} e^{2 x} + e^{2 x} \cdot 2 x^{5})

Solution steps

\frac{d}{d x} (3 x^{5} e^{2 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{5} e^{2 x})

Apply the Product Rule:

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

f = x^{5}, g = e^{2 x}

= 3 (\frac{d}{d x} (x^{5}) e^{2 x} + \frac{d}{d x} (e^{2 x}) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= 3 (5 x^{4} e^{2 x} + e^{2 x} \cdot 2 x^{5})

What is the derivative of f(x)=3x^5e^{2x} ?
The derivative of f(x)=3x^5e^{2x} is 3(5x^4e^{2x}+e^{2x}*2x^5)
What is the first derivative of f(x)=3x^5e^{2x} ?
The first derivative of f(x)=3x^5e^{2x} is 3(5x^4e^{2x}+e^{2x}*2x^5)