What is the derivative of 18xe^{x^2} ?

The derivative of 18xe^{x^2} is 18(e^{x^2}+2e^{x^2}x^2)

What is the first derivative of 18xe^{x^2} ?

The first derivative of 18xe^{x^2} is 18(e^{x^2}+2e^{x^2}x^2)

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\frac{d}{d x} (18 x e^{x^{2}})

18 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

Solution steps

\frac{d}{d x} (18 x e^{x^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 18 \frac{d}{d x} (x e^{x^{2}})

Apply the Product Rule:

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

f = x, g = e^{x^{2}}

= 18 (\frac{d x}{d x} e^{x^{2}} + \frac{d}{d x} (e^{x^{2}}) x)

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

\frac{d}{d x} (e^{x^{2}}) = e^{x^{2}} \cdot 2 x

= 18 (1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx)

Simplify

18 (1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx) : 18 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

= 18 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

What is the derivative of 18xe^{x^2} ?
The derivative of 18xe^{x^2} is 18(e^{x^2}+2e^{x^2}x^2)
What is the first derivative of 18xe^{x^2} ?
The first derivative of 18xe^{x^2} is 18(e^{x^2}+2e^{x^2}x^2)