What is the derivative of 3+x^{10}e^x ?

The derivative of 3+x^{10}e^x is e^xx^{10}+10e^xx^9

What is the first derivative of 3+x^{10}e^x ?

The first derivative of 3+x^{10}e^x is e^xx^{10}+10e^xx^9

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

e^{x} x^{10} + 10 e^{x} x^{9}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (3) = 0

\frac{d}{d x} (x^{10} e^{x}) = 10 x^{9} e^{x} + e^{x} x^{10}

= 0 + 10 x^{9} e^{x} + e^{x} x^{10}

Simplify

= e^{x} x^{10} + 10 e^{x} x^{9}

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What is the derivative of 3+x^{10}e^x ?
The derivative of 3+x^{10}e^x is e^xx^{10}+10e^xx^9
What is the first derivative of 3+x^{10}e^x ?
The first derivative of 3+x^{10}e^x is e^xx^{10}+10e^xx^9