What is the derivative of e^x*x ?

The derivative of e^x*x is e^xx+e^x

What is the first derivative of e^x*x ?

The first derivative of e^x*x is e^xx+e^x

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derivative of

e^{x} \cdot x

e^{x} x + e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

\frac{d x}{d x} = 1

= e^{x} x + 1 \cdot e^{x}

Simplify

= e^{x} x + e^{x}

f (x) = - \frac{12 x}{( x ^{2} + 2 ) ^{\frac{5}{2}}}

n = 1 \sum \infty \frac{1}{n !}

\frac{d}{d x} (2 x sin (3 x))

\frac{\partial}{\partial x} (5 x^{4} y^{7} + 4 x^{8} y^{6})

sin (4 θ)

What is the derivative of e^x*x ?
The derivative of e^x*x is e^xx+e^x
What is the first derivative of e^x*x ?
The first derivative of e^x*x is e^xx+e^x