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Popular >

derivative of f(x)=4x^{10}e^x

Solution

derivative of

f (x) = 4 x^{10} e^{x}

Solution

4 (10 x^{9} e^{x} + e^{x} x^{10})

Solution steps

\frac{d}{d x} (4 x^{10} e^{x})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{10} e^{x})

Apply the Product Rule:

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

f = x^{10}, g = e^{x}

= 4 (\frac{d}{d x} (x^{10}) e^{x} + \frac{d}{d x} (e^{x}) x^{10})

\frac{d}{d x} (x^{10}) = 10 x^{9}

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

= 4 (10 x^{9} e^{x} + e^{x} x^{10})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4x^{10}e^x ?
The derivative of f(x)=4x^{10}e^x is 4(10x^9e^x+e^xx^{10})
What is the first derivative of f(x)=4x^{10}e^x ?
The first derivative of f(x)=4x^{10}e^x is 4(10x^9e^x+e^xx^{10})