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Popular >

derivative of (5x^2-7xe^x)

Solution

\frac{d}{d x} ((5 x^{2} - 7 x) e^{x})

Solution

5 e^{x} x^{2} + 3 e^{x} x - 7 e^{x}

Solution steps

\frac{d}{d x} ((5 x^{2} - 7 x) e^{x})

Apply the Product Rule:

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

f = 5 x^{2} - 7 x, g = e^{x}

= \frac{d}{d x} (5 x^{2} - 7 x) e^{x} + \frac{d}{d x} (e^{x}) (5 x^{2} - 7 x)

\frac{d}{d x} (5 x^{2} - 7 x) = 10 x - 7

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

= (10 x - 7) e^{x} + e^{x} (5 x^{2} - 7 x)

Simplify

(10 x - 7) e^{x} + e^{x} (5 x^{2} - 7 x) : 5 e^{x} x^{2} + 3 e^{x} x - 7 e^{x}

= 5 e^{x} x^{2} + 3 e^{x} x - 7 e^{x}

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Frequently Asked Questions (FAQ)

What is the derivative of (5x^2-7xe^x) ?
The derivative of (5x^2-7xe^x) is 5e^xx^2+3e^xx-7e^x
What is the first derivative of (5x^2-7xe^x) ?
The first derivative of (5x^2-7xe^x) is 5e^xx^2+3e^xx-7e^x