What is the derivative of 2e^{3x^2+6x+7} ?

The derivative of 2e^{3x^2+6x+7} is 2e^{3x^2+6x+7}(6x+6)

What is the first derivative of 2e^{3x^2+6x+7} ?

The first derivative of 2e^{3x^2+6x+7} is 2e^{3x^2+6x+7}(6x+6)

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\frac{d}{d x} (2 e^{3 x^{2} + 6 x + 7})

2 e^{3 x^{2} + 6 x + 7} (6 x + 6)

Solution steps

\frac{d}{d x} (2 e^{3 x^{2} + 6 x + 7})

Take the constant out:

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

= 2 \frac{d}{d x} (e^{3 x^{2} + 6 x + 7})

Apply the chain rule:

e^{3 x^{2} + 6 x + 7} \frac{d}{d x} (3 x^{2} + 6 x + 7)

= e^{3 x^{2} + 6 x + 7} \frac{d}{d x} (3 x^{2} + 6 x + 7)

\frac{d}{d x} (3 x^{2} + 6 x + 7) = 6 x + 6

= 2 e^{3 x^{2} + 6 x + 7} (6 x + 6)

What is the derivative of 2e^{3x^2+6x+7} ?
The derivative of 2e^{3x^2+6x+7} is 2e^{3x^2+6x+7}(6x+6)
What is the first derivative of 2e^{3x^2+6x+7} ?
The first derivative of 2e^{3x^2+6x+7} is 2e^{3x^2+6x+7}(6x+6)