What is the derivative of f(x)=(x^3+2x)e^x ?

The derivative of f(x)=(x^3+2x)e^x is (3x^2+2)e^x+e^x(x^3+2x)

What is the first derivative of f(x)=(x^3+2x)e^x ?

The first derivative of f(x)=(x^3+2x)e^x is (3x^2+2)e^x+e^x(x^3+2x)

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derivative

(3 x^{2} + 2) e^{x} + e^{x} (x^{3} + 2 x)

Solution steps

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

Apply the Product Rule:

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

f = x^{3} + 2 x, g = e^{x}

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

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

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

= (3 x^{2} + 2) e^{x} + e^{x} (x^{3} + 2 x)

What is the derivative of f(x)=(x^3+2x)e^x ?
The derivative of f(x)=(x^3+2x)e^x is (3x^2+2)e^x+e^x(x^3+2x)
What is the first derivative of f(x)=(x^3+2x)e^x ?
The first derivative of f(x)=(x^3+2x)e^x is (3x^2+2)e^x+e^x(x^3+2x)