What is the derivative of 4xe^{x^2-1} ?

The derivative of 4xe^{x^2-1} is 4(e^{x^2-1}+2e^{x^2-1}x^2)

What is the first derivative of 4xe^{x^2-1} ?

The first derivative of 4xe^{x^2-1} is 4(e^{x^2-1}+2e^{x^2-1}x^2)

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derivative of

4 x e^{x^{2} - 1}

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

Solution steps

\frac{d}{d x} (4 x e^{x^{2} - 1})

Take the constant out:

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

= 4 \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}

= 4 (\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

= 4 (1 \cdot e^{x^{2} - 1} + e^{x^{2} - 1} \cdot 2 xx)

Simplify

4 (1 \cdot e^{x^{2} - 1} + e^{x^{2} - 1} \cdot 2 xx) : 4 (e^{x^{2} - 1} + 2 e^{x^{2} - 1} x^{2})

= 4 (e^{x^{2} - 1} + 2 e^{x^{2} - 1} x^{2})

f (x) = \frac{2}{3 x} - \frac{1}{6 x}

sin (x), π

\frac{d P}{d t} = P (850 - P)

\frac{d y}{d x} = - y

y^{^{'}} + \frac{5}{x} y = 0

What is the derivative of 4xe^{x^2-1} ?
The derivative of 4xe^{x^2-1} is 4(e^{x^2-1}+2e^{x^2-1}x^2)
What is the first derivative of 4xe^{x^2-1} ?
The first derivative of 4xe^{x^2-1} is 4(e^{x^2-1}+2e^{x^2-1}x^2)