What is the derivative of f(x)=x^4e^{2x} ?

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

What is the first derivative of f(x)=x^4e^{2x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = x^{4} e^{2 x}

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

Solution steps

\frac{d}{d x} (x^{4} e^{2 x})

Apply the Product Rule:

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

f = x^{4}, g = e^{2 x}

= \frac{d}{d x} (x^{4}) e^{2 x} + \frac{d}{d x} (e^{2 x}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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

4 x + \frac{16}{x ^{2}}

\int_{0}^{1} x^{2} e^{x^{3}} d x

\frac{d y}{d x} = - 0.5 y + x

\int \frac{x}{3} d x

y^{^{''}} + 3 y = - 9

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