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Popular >

derivative of 6x^9e^x

Solution

derivative of

6 x^{9} e^{x}

Solution

6 (9 x^{8} e^{x} + e^{x} x^{9})

Solution steps

\frac{d}{d x} (6 x^{9} e^{x})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{9} e^{x})

Apply the Product Rule:

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

f = x^{9}, g = e^{x}

= 6 (\frac{d}{d x} (x^{9}) e^{x} + \frac{d}{d x} (e^{x}) x^{9})

\frac{d}{d x} (x^{9}) = 9 x^{8}

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

= 6 (9 x^{8} e^{x} + e^{x} x^{9})

Popular Examples

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\frac{d}{d x} ((1 - x - x^{3}) (1 - x + x^{3}))

(\partial)/(\partial x)(ln(y-x)-x/(y-x))

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\int_{- 6}^{- 10} \frac{1}{x + 2} d x

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Frequently Asked Questions (FAQ)

What is the derivative of 6x^9e^x ?
The derivative of 6x^9e^x is 6(9x^8e^x+e^xx^9)
What is the first derivative of 6x^9e^x ?
The first derivative of 6x^9e^x is 6(9x^8e^x+e^xx^9)