What is the derivative of e^{4x^2}*8x ?

The derivative of e^{4x^2}*8x is 8(8e^{4x^2}x^2+e^{4x^2})

What is the first derivative of e^{4x^2}*8x ?

The first derivative of e^{4x^2}*8x is 8(8e^{4x^2}x^2+e^{4x^2})

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\frac{d}{d x} (e^{4 x^{2}} \cdot 8 x)

8 (8 e^{4 x^{2}} x^{2} + e^{4 x^{2}})

Solution steps

\frac{d}{d x} (e^{4 x^{2}} \cdot 8 x)

Take the constant out:

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

= 8 \frac{d}{d x} (e^{4 x^{2}} x)

Apply the Product Rule:

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

f = e^{4 x^{2}}, g = x

= 8 (\frac{d}{d x} (e^{4 x^{2}}) x + \frac{d x}{d x} e^{4 x^{2}})

\frac{d}{d x} (e^{4 x^{2}}) = e^{4 x^{2}} \cdot 8 x

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

= 8 (e^{4 x^{2}} \cdot 8 xx + 1 \cdot e^{4 x^{2}})

Simplify

8 (e^{4 x^{2}} \cdot 8 xx + 1 \cdot e^{4 x^{2}}) : 8 (8 e^{4 x^{2}} x^{2} + e^{4 x^{2}})

= 8 (8 e^{4 x^{2}} x^{2} + e^{4 x^{2}})

What is the derivative of e^{4x^2}*8x ?
The derivative of e^{4x^2}*8x is 8(8e^{4x^2}x^2+e^{4x^2})
What is the first derivative of e^{4x^2}*8x ?
The first derivative of e^{4x^2}*8x is 8(8e^{4x^2}x^2+e^{4x^2})