What is the derivative of e^xx^5+10e^xx^4+20e^xx^3 ?

The derivative of e^xx^5+10e^xx^4+20e^xx^3 is e^xx^5+15e^xx^4+60e^xx^3+60e^xx^2

What is the first derivative of e^xx^5+10e^xx^4+20e^xx^3 ?

The first derivative of e^xx^5+10e^xx^4+20e^xx^3 is e^xx^5+15e^xx^4+60e^xx^3+60e^xx^2

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\frac{d}{d x} (e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3})

e^{x} x^{5} + 15 e^{x} x^{4} + 60 e^{x} x^{3} + 60 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{x} x^{5}) + \frac{d}{d x} (10 e^{x} x^{4}) + \frac{d}{d x} (20 e^{x} x^{3})

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

\frac{d}{d x} (10 e^{x} x^{4}) = 10 (e^{x} x^{4} + 4 x^{3} e^{x})

\frac{d}{d x} (20 e^{x} x^{3}) = 20 (e^{x} x^{3} + 3 x^{2} e^{x})

= e^{x} x^{5} + 5 x^{4} e^{x} + 10 (e^{x} x^{4} + 4 x^{3} e^{x}) + 20 (e^{x} x^{3} + 3 x^{2} e^{x})

Simplify

e^{x} x^{5} + 5 x^{4} e^{x} + 10 (e^{x} x^{4} + 4 x^{3} e^{x}) + 20 (e^{x} x^{3} + 3 x^{2} e^{x}) : e^{x} x^{5} + 15 e^{x} x^{4} + 60 e^{x} x^{3} + 60 e^{x} x^{2}

= e^{x} x^{5} + 15 e^{x} x^{4} + 60 e^{x} x^{3} + 60 e^{x} x^{2}

What is the derivative of e^xx^5+10e^xx^4+20e^xx^3 ?
The derivative of e^xx^5+10e^xx^4+20e^xx^3 is e^xx^5+15e^xx^4+60e^xx^3+60e^xx^2
What is the first derivative of e^xx^5+10e^xx^4+20e^xx^3 ?
The first derivative of e^xx^5+10e^xx^4+20e^xx^3 is e^xx^5+15e^xx^4+60e^xx^3+60e^xx^2