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

The derivative of (x^3+4e^{3x}) is 3x^2e^{3x}+e^{3x}*3(x^3+4)

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

The first derivative of (x^3+4e^{3x}) is 3x^2e^{3x}+e^{3x}*3(x^3+4)

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

3 x^{2} e^{3 x} + e^{3 x} \cdot 3 (x^{3} + 4)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{3} + 4) = 3 x^{2}

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

= 3 x^{2} e^{3 x} + e^{3 x} \cdot 3 (x^{3} + 4)

What is the derivative of (x^3+4e^{3x}) ?
The derivative of (x^3+4e^{3x}) is 3x^2e^{3x}+e^{3x}*3(x^3+4)
What is the first derivative of (x^3+4e^{3x}) ?
The first derivative of (x^3+4e^{3x}) is 3x^2e^{3x}+e^{3x}*3(x^3+4)