What is the derivative of f(x)=(x^4-4x)e^x ?

The derivative of f(x)=(x^4-4x)e^x is (4x^3-4)e^x+e^x(x^4-4x)

What is the first derivative of f(x)=(x^4-4x)e^x ?

The first derivative of f(x)=(x^4-4x)e^x is (4x^3-4)e^x+e^x(x^4-4x)

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} - 4 x) e^{x}

(4 x^{3} - 4) e^{x} + e^{x} (x^{4} - 4 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= (4 x^{3} - 4) e^{x} + e^{x} (x^{4} - 4 x)

- \frac{8}{x ^{9}}

\int (x^{4} + 2 x - 9) ln (x) d x

\frac{3}{x + 1}

t y^{^{'}} + 2 y = sin (t), y (\frac{π}{2}) = 3

y^{^{'}} = y (3 - y t)

What is the derivative of f(x)=(x^4-4x)e^x ?
The derivative of f(x)=(x^4-4x)e^x is (4x^3-4)e^x+e^x(x^4-4x)
What is the first derivative of f(x)=(x^4-4x)e^x ?
The first derivative of f(x)=(x^4-4x)e^x is (4x^3-4)e^x+e^x(x^4-4x)