What is the derivative of e^xx^7+14e^xx^6+42e^xx^5 ?

The derivative of e^xx^7+14e^xx^6+42e^xx^5 is e^xx^7+21e^xx^6+126e^xx^5+210e^xx^4

What is the first derivative of e^xx^7+14e^xx^6+42e^xx^5 ?

The first derivative of e^xx^7+14e^xx^6+42e^xx^5 is e^xx^7+21e^xx^6+126e^xx^5+210e^xx^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

e^{x} x^{7} + 14 e^{x} x^{6} + 42 e^{x} x^{5}

e^{x} x^{7} + 21 e^{x} x^{6} + 126 e^{x} x^{5} + 210 e^{x} x^{4}

Solution steps

\frac{d}{d x} (e^{x} x^{7} + 14 e^{x} x^{6} + 42 e^{x} x^{5})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{x} x^{7}) + \frac{d}{d x} (14 e^{x} x^{6}) + \frac{d}{d x} (42 e^{x} x^{5})

\frac{d}{d x} (e^{x} x^{7}) = e^{x} x^{7} + 7 x^{6} e^{x}

\frac{d}{d x} (14 e^{x} x^{6}) = 14 (e^{x} x^{6} + 6 x^{5} e^{x})

\frac{d}{d x} (42 e^{x} x^{5}) = 42 (e^{x} x^{5} + 5 x^{4} e^{x})

= e^{x} x^{7} + 7 x^{6} e^{x} + 14 (e^{x} x^{6} + 6 x^{5} e^{x}) + 42 (e^{x} x^{5} + 5 x^{4} e^{x})

Simplify

e^{x} x^{7} + 7 x^{6} e^{x} + 14 (e^{x} x^{6} + 6 x^{5} e^{x}) + 42 (e^{x} x^{5} + 5 x^{4} e^{x}) : e^{x} x^{7} + 21 e^{x} x^{6} + 126 e^{x} x^{5} + 210 e^{x} x^{4}

= e^{x} x^{7} + 21 e^{x} x^{6} + 126 e^{x} x^{5} + 210 e^{x} x^{4}

What is the derivative of e^xx^7+14e^xx^6+42e^xx^5 ?
The derivative of e^xx^7+14e^xx^6+42e^xx^5 is e^xx^7+21e^xx^6+126e^xx^5+210e^xx^4
What is the first derivative of e^xx^7+14e^xx^6+42e^xx^5 ?
The first derivative of e^xx^7+14e^xx^6+42e^xx^5 is e^xx^7+21e^xx^6+126e^xx^5+210e^xx^4