What is the derivative of e^xx^6+12e^xx^5+30e^xx^4 ?

The derivative of e^xx^6+12e^xx^5+30e^xx^4 is e^xx^6+18e^xx^5+90e^xx^4+120e^xx^3

What is the first derivative of e^xx^6+12e^xx^5+30e^xx^4 ?

The first derivative of e^xx^6+12e^xx^5+30e^xx^4 is e^xx^6+18e^xx^5+90e^xx^4+120e^xx^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (e^{x} x^{6} + 12 e^{x} x^{5} + 30 e^{x} x^{4})

e^{x} x^{6} + 18 e^{x} x^{5} + 90 e^{x} x^{4} + 120 e^{x} x^{3}

Solution steps

\frac{d}{d x} (e^{x} x^{6} + 12 e^{x} x^{5} + 30 e^{x} x^{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{x} x^{6}) + \frac{d}{d x} (12 e^{x} x^{5}) + \frac{d}{d x} (30 e^{x} x^{4})

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

\frac{d}{d x} (12 e^{x} x^{5}) = 12 (e^{x} x^{5} + 5 x^{4} e^{x})

\frac{d}{d x} (30 e^{x} x^{4}) = 30 (e^{x} x^{4} + 4 x^{3} e^{x})

= e^{x} x^{6} + 6 x^{5} e^{x} + 12 (e^{x} x^{5} + 5 x^{4} e^{x}) + 30 (e^{x} x^{4} + 4 x^{3} e^{x})

Simplify

e^{x} x^{6} + 6 x^{5} e^{x} + 12 (e^{x} x^{5} + 5 x^{4} e^{x}) + 30 (e^{x} x^{4} + 4 x^{3} e^{x}) : e^{x} x^{6} + 18 e^{x} x^{5} + 90 e^{x} x^{4} + 120 e^{x} x^{3}

= e^{x} x^{6} + 18 e^{x} x^{5} + 90 e^{x} x^{4} + 120 e^{x} x^{3}

\int (2 + 5) d x

\frac{1}{1 - x ^{2}}

\int cos (t) d t

\int_{- 64}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

\frac{\partial}{\partial y} (x^{3} + 3 x^{2} y - 2 y^{2})

What is the derivative of e^xx^6+12e^xx^5+30e^xx^4 ?
The derivative of e^xx^6+12e^xx^5+30e^xx^4 is e^xx^6+18e^xx^5+90e^xx^4+120e^xx^3
What is the first derivative of e^xx^6+12e^xx^5+30e^xx^4 ?
The first derivative of e^xx^6+12e^xx^5+30e^xx^4 is e^xx^6+18e^xx^5+90e^xx^4+120e^xx^3