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Popular >

derivative of (3x^2+5xe^x)

Solution

\frac{d}{d x} ((3 x^{2} + 5 x) e^{x})

Solution

3 e^{x} x^{2} + 11 e^{x} x + 5 e^{x}

Solution steps

\frac{d}{d x} ((3 x^{2} + 5 x) e^{x})

Apply the Product Rule:

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

f = 3 x^{2} + 5 x, g = e^{x}

= \frac{d}{d x} (3 x^{2} + 5 x) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} + 5 x)

\frac{d}{d x} (3 x^{2} + 5 x) = 6 x + 5

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

= (6 x + 5) e^{x} + e^{x} (3 x^{2} + 5 x)

Simplify

(6 x + 5) e^{x} + e^{x} (3 x^{2} + 5 x) : 3 e^{x} x^{2} + 11 e^{x} x + 5 e^{x}

= 3 e^{x} x^{2} + 11 e^{x} x + 5 e^{x}

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^2+5xe^x) ?
The derivative of (3x^2+5xe^x) is 3e^xx^2+11e^xx+5e^x
What is the first derivative of (3x^2+5xe^x) ?
The first derivative of (3x^2+5xe^x) is 3e^xx^2+11e^xx+5e^x