What is the derivative of x^8e^{4x} ?

The derivative of x^8e^{4x} is 8x^7e^{4x}+e^{4x}*4x^8

What is the first derivative of x^8e^{4x} ?

The first derivative of x^8e^{4x} is 8x^7e^{4x}+e^{4x}*4x^8

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\frac{d}{d x} (x^{8} e^{4 x})

8 x^{7} e^{4 x} + e^{4 x} \cdot 4 x^{8}

Solution steps

\frac{d}{d x} (x^{8} e^{4 x})

Apply the Product Rule:

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

f = x^{8}, g = e^{4 x}

= \frac{d}{d x} (x^{8}) e^{4 x} + \frac{d}{d x} (e^{4 x}) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

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

= 8 x^{7} e^{4 x} + e^{4 x} \cdot 4 x^{8}

\frac{d}{d x} (cos (0))

(3 x - 2)^{2} (x^{4} + 2)^{2}

\int \frac{2}{3} (1 - x)^{\frac{3}{2}} (1) d x

\frac{d}{d x} (\frac{6 x}{5 - tan ( x )})

y^{^{''}} - 3 y^{^{'}} + 2 = e^{t}

What is the derivative of x^8e^{4x} ?
The derivative of x^8e^{4x} is 8x^7e^{4x}+e^{4x}*4x^8
What is the first derivative of x^8e^{4x} ?
The first derivative of x^8e^{4x} is 8x^7e^{4x}+e^{4x}*4x^8