What is the derivative of e^{3x^2}*6x ?

The derivative of e^{3x^2}*6x is 6(6e^{3x^2}x^2+e^{3x^2})

What is the first derivative of e^{3x^2}*6x ?

The first derivative of e^{3x^2}*6x is 6(6e^{3x^2}x^2+e^{3x^2})

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\frac{d}{d x} (e^{3 x^{2}} \cdot 6 x)

6 (6 e^{3 x^{2}} x^{2} + e^{3 x^{2}})

Solution steps

\frac{d}{d x} (e^{3 x^{2}} \cdot 6 x)

Take the constant out:

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

= 6 \frac{d}{d x} (e^{3 x^{2}} x)

Apply the Product Rule:

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

f = e^{3 x^{2}}, g = x

= 6 (\frac{d}{d x} (e^{3 x^{2}}) x + \frac{d x}{d x} e^{3 x^{2}})

\frac{d}{d x} (e^{3 x^{2}}) = e^{3 x^{2}} \cdot 6 x

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

= 6 (e^{3 x^{2}} \cdot 6 xx + 1 \cdot e^{3 x^{2}})

Simplify

6 (e^{3 x^{2}} \cdot 6 xx + 1 \cdot e^{3 x^{2}}) : 6 (6 e^{3 x^{2}} x^{2} + e^{3 x^{2}})

= 6 (6 e^{3 x^{2}} x^{2} + e^{3 x^{2}})

y = 2 x^{3} + 3 x^{2} - 12 x + 6

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} + y = 1

x \to 2 lim (- 10 x + (10))

f (x) = 28 x - 0.01 x^{2}

3 x^{2} - 5 y^{2} = 4

What is the derivative of e^{3x^2}*6x ?
The derivative of e^{3x^2}*6x is 6(6e^{3x^2}x^2+e^{3x^2})
What is the first derivative of e^{3x^2}*6x ?
The first derivative of e^{3x^2}*6x is 6(6e^{3x^2}x^2+e^{3x^2})