What is the derivative of x^5e^{7x} ?

The derivative of x^5e^{7x} is 5x^4e^{7x}+e^{7x}*7x^5

What is the first derivative of x^5e^{7x} ?

The first derivative of x^5e^{7x} is 5x^4e^{7x}+e^{7x}*7x^5

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\frac{d}{d x} (x^{5} e^{7 x})

5 x^{4} e^{7 x} + e^{7 x} \cdot 7 x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{7 x})

Apply the Product Rule:

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

f = x^{5}, g = e^{7 x}

= \frac{d}{d x} (x^{5}) e^{7 x} + \frac{d}{d x} (e^{7 x}) x^{5}

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

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= 5 x^{4} e^{7 x} + e^{7 x} \cdot 7 x^{5}

x \to 1 lim ((x - 1)^{3 x - 3})

x \to 2 lim (x 13 - x^{2})

\frac{d}{d x} (x cos (x^{3}))

\frac{d}{d x} (\frac{5 x ^{6}}{2} + \frac{12}{7 x ^{5}} - x)

\int \frac{4 x}{x - 8} d x

What is the derivative of x^5e^{7x} ?
The derivative of x^5e^{7x} is 5x^4e^{7x}+e^{7x}*7x^5
What is the first derivative of x^5e^{7x} ?
The first derivative of x^5e^{7x} is 5x^4e^{7x}+e^{7x}*7x^5