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

The derivative of x^4e^{4x} is 4x^3e^{4x}+e^{4x}*4x^4

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

The first derivative of x^4e^{4x} is 4x^3e^{4x}+e^{4x}*4x^4

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

4 x^{3} e^{4 x} + e^{4 x} \cdot 4 x^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} e^{4 x} + e^{4 x} \cdot 4 x^{4}

y^{^{'}} = y (x y^{4} - 1)

x^{2} \frac{d y}{d x} + x y = x^{3} + 1

\frac{d}{d x} (2 x + 6)

x \to \infty lim (\frac{x}{x ^{3} + 6})

\frac{\partial}{\partial x} (ln (x + z))

What is the derivative of x^4e^{4x} ?
The derivative of x^4e^{4x} is 4x^3e^{4x}+e^{4x}*4x^4
What is the first derivative of x^4e^{4x} ?
The first derivative of x^4e^{4x} is 4x^3e^{4x}+e^{4x}*4x^4