What is the derivative of (x-4e^{3x}) ?

The derivative of (x-4e^{3x}) is 3e^{3x}x-11e^{3x}

What is the first derivative of (x-4e^{3x}) ?

The first derivative of (x-4e^{3x}) is 3e^{3x}x-11e^{3x}

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\frac{d}{d x} ((x - 4) e^{3 x})

3 e^{3 x} x - 11 e^{3 x}

Solution steps

\frac{d}{d x} ((x - 4) e^{3 x})

Apply the Product Rule:

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

f = x - 4, g = e^{3 x}

= \frac{d}{d x} (x - 4) e^{3 x} + \frac{d}{d x} (e^{3 x}) (x - 4)

\frac{d}{d x} (x - 4) = 1

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

= 1 \cdot e^{3 x} + e^{3 x} \cdot 3 (x - 4)

Simplify

1 \cdot e^{3 x} + e^{3 x} \cdot 3 (x - 4) : 3 e^{3 x} x - 11 e^{3 x}

= 3 e^{3 x} x - 11 e^{3 x}

e^{- 2 x}

x \to 0 lim (coth (x))

3 x^{2} + 4

\frac{1}{1 - x}

\frac{d}{d x} (\frac{2 x ^{3}}{x ^{2} - 3})

What is the derivative of (x-4e^{3x}) ?
The derivative of (x-4e^{3x}) is 3e^{3x}x-11e^{3x}
What is the first derivative of (x-4e^{3x}) ?
The first derivative of (x-4e^{3x}) is 3e^{3x}x-11e^{3x}