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Popular >

derivative of (x^3-4x*e^{3x})

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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