What is the derivative of ({f}(x)(xe^x)) ?

The derivative of ({f}(x)(xe^x)) is derivative of {f}(x)xe^x+(e^x+e^xx){f}(x)

What is the first derivative of ({f}(x)(xe^x)) ?

The first derivative of ({f}(x)(xe^x)) is derivative of {f}(x)xe^x+(e^x+e^xx){f}(x)

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

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

Solution steps

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

Apply the Product Rule:

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

f = f (x), g = x e^{x}

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

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

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

3 x^{3.4} - 10 x^{2.2} + 8 x

3 k^{(2)} - 3 y^{(2)} x - k^{(3)} 2 y x

\frac{e ^{3} + 1}{5}

x ln (6) + 2 x ln (75)

x - 0.36 x^{1024}

What is the derivative of ({f}(x)(xe^x)) ?
The derivative of ({f}(x)(xe^x)) is derivative of {f}(x)xe^x+(e^x+e^xx){f}(x)
What is the first derivative of ({f}(x)(xe^x)) ?
The first derivative of ({f}(x)(xe^x)) is derivative of {f}(x)xe^x+(e^x+e^xx){f}(x)