What is the derivative of Ae^{3x}+3Axe^{3x} ?

The derivative of Ae^{3x}+3Axe^{3x} is 6Ae^{3x}+9Ae^{3x}x

What is the first derivative of Ae^{3x}+3Axe^{3x} ?

The first derivative of Ae^{3x}+3Axe^{3x} is 6Ae^{3x}+9Ae^{3x}x

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

6 A e^{3 x} + 9 A e^{3 x} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= 6 A e^{3 x} + 9 A e^{3 x} x

What is the derivative of Ae^{3x}+3Axe^{3x} ?
The derivative of Ae^{3x}+3Axe^{3x} is 6Ae^{3x}+9Ae^{3x}x
What is the first derivative of Ae^{3x}+3Axe^{3x} ?
The first derivative of Ae^{3x}+3Axe^{3x} is 6Ae^{3x}+9Ae^{3x}x