What is the derivative of 6x^5e^x+e^xx^6 ?

The derivative of 6x^5e^x+e^xx^6 is e^xx^6+12e^xx^5+30e^xx^4

What is the first derivative of 6x^5e^x+e^xx^6 ?

The first derivative of 6x^5e^x+e^xx^6 is e^xx^6+12e^xx^5+30e^xx^4

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derivative of

6 x^{5} e^{x} + e^{x} x^{6}

e^{x} x^{6} + 12 e^{x} x^{5} + 30 e^{x} x^{4}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

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