What is the derivative of 5x^4e^x+e^xx^5 ?

The derivative of 5x^4e^x+e^xx^5 is e^xx^5+10e^xx^4+20e^xx^3

What is the first derivative of 5x^4e^x+e^xx^5 ?

The first derivative of 5x^4e^x+e^xx^5 is e^xx^5+10e^xx^4+20e^xx^3

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derivative of

5 x^{4} e^{x} + e^{x} x^{5}

e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

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