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Popular >

derivative of 4x^6e^x

Solution

derivative of

4 x^{6} e^{x}

Solution

4 (6 x^{5} e^{x} + e^{x} x^{6})

Solution steps

\frac{d}{d x} (4 x^{6} e^{x})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{6} e^{x})

Apply the Product Rule:

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

f = x^{6}, g = e^{x}

= 4 (\frac{d}{d x} (x^{6}) e^{x} + \frac{d}{d x} (e^{x}) x^{6})

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

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

= 4 (6 x^{5} e^{x} + e^{x} x^{6})

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Frequently Asked Questions (FAQ)

What is the derivative of 4x^6e^x ?
The derivative of 4x^6e^x is 4(6x^5e^x+e^xx^6)
What is the first derivative of 4x^6e^x ?
The first derivative of 4x^6e^x is 4(6x^5e^x+e^xx^6)