What is the derivative of Cxe^{3x} ?

The derivative of Cxe^{3x} is C(e^{3x}+3e^{3x}x)

What is the first derivative of Cxe^{3x} ?

The first derivative of Cxe^{3x} is C(e^{3x}+3e^{3x}x)

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\frac{d}{d x} (C x e^{3 x})

C (e^{3 x} + 3 e^{3 x} x)

Solution steps

\frac{d}{d x} (C x e^{3 x})

Treat

C

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= C (1 \cdot e^{3 x} + e^{3 x} \cdot 3 x)

Simplify

= C (e^{3 x} + 3 e^{3 x} x)

8 t sin (π t)

\frac{d}{d x} (\frac{2 x - 1}{5 - 4 x})

(\frac{22.2 sin ( 5 t )}{t}) + 44

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n = 3 \sum \infty \frac{1}{4 ^{n}}

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