What is the derivative of f(x)=6x^9e^x ?

The derivative of f(x)=6x^9e^x is 6(9x^8e^x+e^xx^9)

What is the first derivative of f(x)=6x^9e^x ?

The first derivative of f(x)=6x^9e^x is 6(9x^8e^x+e^xx^9)

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derivative of

f (x) = 6 x^{9} e^{x}

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})

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