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

The derivative of 2(e^{3x}+3e^{3x}x) is 2(9e^{3x}x+6e^{3x})

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

The first derivative of 2(e^{3x}+3e^{3x}x) is 2(9e^{3x}x+6e^{3x})

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

2 (9 e^{3 x} x + 6 e^{3 x})

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Expand

e^{3 x} \cdot 3 + 3 (3 e^{3 x} x + e^{3 x}) : 9 e^{3 x} x + 6 e^{3 x}

= 2 (9 e^{3 x} x + 6 e^{3 x})

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x \to 0 lim (\frac{x ^{3} + 4}{x - 2})

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f (x) = 2 x^{4} - 5 x^{\frac{7}{2}} + 3

What is the derivative of 2(e^{3x}+3e^{3x}x) ?
The derivative of 2(e^{3x}+3e^{3x}x) is 2(9e^{3x}x+6e^{3x})
What is the first derivative of 2(e^{3x}+3e^{3x}x) ?
The first derivative of 2(e^{3x}+3e^{3x}x) is 2(9e^{3x}x+6e^{3x})