What is the derivative of x^{19}e^x ?

The derivative of x^{19}e^x is 19x^{18}e^x+e^xx^{19}

What is the first derivative of x^{19}e^x ?

The first derivative of x^{19}e^x is 19x^{18}e^x+e^xx^{19}

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derivative of

x^{19} e^{x}

19 x^{18} e^{x} + e^{x} x^{19}

Solution steps

\frac{d}{d x} (x^{19} e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{19}, g = e^{x}

= \frac{d}{d x} (x^{19}) e^{x} + \frac{d}{d x} (e^{x}) x^{19}

\frac{d}{d x} (x^{19}) = 19 x^{18}

\frac{d}{d x} (e^{x}) = e^{x}

= 19 x^{18} e^{x} + e^{x} x^{19}

\frac{\partial}{\partial x} (x^{2} - 1)

\frac{d}{d x} ((x^{2} + 5 x) e^{x})

\int x^{2} y d y

\int 4 tan (t) d t

\int \frac{4 x}{1 - x ^{4}} d x

What is the derivative of x^{19}e^x ?
The derivative of x^{19}e^x is 19x^{18}e^x+e^xx^{19}
What is the first derivative of x^{19}e^x ?
The first derivative of x^{19}e^x is 19x^{18}e^x+e^xx^{19}