What is the derivative of x^4e^{5x} ?

The derivative of x^4e^{5x} is 4x^3e^{5x}+e^{5x}*5x^4

What is the first derivative of x^4e^{5x} ?

The first derivative of x^4e^{5x} is 4x^3e^{5x}+e^{5x}*5x^4

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\frac{d}{d x} (x^{4} e^{5 x})

4 x^{3} e^{5 x} + e^{5 x} \cdot 5 x^{4}

Solution steps

\frac{d}{d x} (x^{4} e^{5 x})

Apply the Product Rule:

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

f = x^{4}, g = e^{5 x}

= \frac{d}{d x} (x^{4}) e^{5 x} + \frac{d}{d x} (e^{5 x}) x^{4}

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

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= 4 x^{3} e^{5 x} + e^{5 x} \cdot 5 x^{4}

\int 2 sin (3 x) + 3 sin (2 x) d x

\frac{d}{d x} (ln (cosh (4 x)))

\int tan^{2} (2 y) d y

\frac{d}{d x} ((x + 5)^{2})

x \to \infty lim (3 x - 1)

What is the derivative of x^4e^{5x} ?
The derivative of x^4e^{5x} is 4x^3e^{5x}+e^{5x}*5x^4
What is the first derivative of x^4e^{5x} ?
The first derivative of x^4e^{5x} is 4x^3e^{5x}+e^{5x}*5x^4