What is the derivative of 2xe^{x^2-1} ?

The derivative of 2xe^{x^2-1} is 2(e^{x^2-1}+2e^{x^2-1}x^2)

What is the first derivative of 2xe^{x^2-1} ?

The first derivative of 2xe^{x^2-1} is 2(e^{x^2-1}+2e^{x^2-1}x^2)

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\frac{d}{d x} (2 x e^{x^{2} - 1})

2 (e^{x^{2} - 1} + 2 e^{x^{2} - 1} x^{2})

Solution steps

\frac{d}{d x} (2 x e^{x^{2} - 1})

Take the constant out:

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

= 2 \frac{d}{d x} (x e^{x^{2} - 1})

Apply the Product Rule:

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

f = x, g = e^{x^{2} - 1}

= 2 (\frac{d x}{d x} e^{x^{2} - 1} + \frac{d}{d x} (e^{x^{2} - 1}) x)

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

\frac{d}{d x} (e^{x^{2} - 1}) = e^{x^{2} - 1} \cdot 2 x

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

Simplify

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

= 2 (e^{x^{2} - 1} + 2 e^{x^{2} - 1} x^{2})

f (30) = \frac{850}{d}

\frac{d}{d x} (\frac{5}{x + 7})

x \to - 2 lim (\frac{x + 1}{x ^{2} - 2})

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

\int \frac{1 - y}{y ^{2}} d y

What is the derivative of 2xe^{x^2-1} ?
The derivative of 2xe^{x^2-1} is 2(e^{x^2-1}+2e^{x^2-1}x^2)
What is the first derivative of 2xe^{x^2-1} ?
The first derivative of 2xe^{x^2-1} is 2(e^{x^2-1}+2e^{x^2-1}x^2)