What is the derivative of 6xe^{x^2} ?

The derivative of 6xe^{x^2} is 6(e^{x^2}+2e^{x^2}x^2)

What is the first derivative of 6xe^{x^2} ?

The first derivative of 6xe^{x^2} is 6(e^{x^2}+2e^{x^2}x^2)

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\frac{d}{d x} (6 x e^{x^{2}})

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

Solution steps

\frac{d}{d x} (6 x e^{x^{2}})

Take the constant out:

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

= 6 \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}}

= 6 (\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

= 6 (1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx)

Simplify

6 (1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx) : 6 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

= 6 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

x \to 2 lim (x^{2} - 6 x + 3)

\frac{d}{d x} (\frac{1}{1 + e ^{0.5 x}})

n = 1 \sum \infty n e^{- 6 n}

\frac{d ^{2}}{d z ^{2}} (z^{2} e^{z})

\int (x^{2} + 1) d x

What is the derivative of 6xe^{x^2} ?
The derivative of 6xe^{x^2} is 6(e^{x^2}+2e^{x^2}x^2)
What is the first derivative of 6xe^{x^2} ?
The first derivative of 6xe^{x^2} is 6(e^{x^2}+2e^{x^2}x^2)