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Popular >

derivative of 5x^2e^{3x}

Solution

derivative of

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of 5x^2e^{3x} ?
The derivative of 5x^2e^{3x} is 5(2xe^{3x}+e^{3x}*3x^2)
What is the first derivative of 5x^2e^{3x} ?
The first derivative of 5x^2e^{3x} is 5(2xe^{3x}+e^{3x}*3x^2)