What is the derivative of x^5e^{6x} ?

The derivative of x^5e^{6x} is 5x^4e^{6x}+e^{6x}*6x^5

What is the first derivative of x^5e^{6x} ?

The first derivative of x^5e^{6x} is 5x^4e^{6x}+e^{6x}*6x^5

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\frac{d}{d x} (x^{5} e^{6 x})

5 x^{4} e^{6 x} + e^{6 x} \cdot 6 x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{6 x})

Apply the Product Rule:

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

f = x^{5}, g = e^{6 x}

= \frac{d}{d x} (x^{5}) e^{6 x} + \frac{d}{d x} (e^{6 x}) x^{5}

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 5 x^{4} e^{6 x} + e^{6 x} \cdot 6 x^{5}

x \to \infty lim (\frac{2}{x})

\frac{d}{d x} (- 2 cos (3 x))

x \to 0 + lim (\frac{x}{3 x} - 7 x)

\int \frac{3}{91} x^{2} d x

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

What is the derivative of x^5e^{6x} ?
The derivative of x^5e^{6x} is 5x^4e^{6x}+e^{6x}*6x^5
What is the first derivative of x^5e^{6x} ?
The first derivative of x^5e^{6x} is 5x^4e^{6x}+e^{6x}*6x^5