What is the derivative of x5^x ?

The derivative of x5^x is 5^x+ln(5)*5^xx

What is the first derivative of x5^x ?

The first derivative of x5^x is 5^x+ln(5)*5^xx

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derivative of

x 5^{x}

5^{x} + ln (5) \cdot 5^{x} x

Solution steps

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

Apply the Product Rule:

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

f = x, g = 5^{x}

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

\frac{d x}{d x} = 1

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

= 1 \cdot 5^{x} + 5^{x} ln (5) x

Simplify

= 5^{x} + ln (5) \cdot 5^{x} x

\frac{2}{x}, at x = 3

\int \frac{2}{2 x + 1} d x

\int (e^{x})^{2} d x

n = 1 \sum \infty 23 (\frac{2}{5})^{n}

\int \frac{e ^{x}}{3 - e ^{2 x}} d x

What is the derivative of x5^x ?
The derivative of x5^x is 5^x+ln(5)*5^xx
What is the first derivative of x5^x ?
The first derivative of x5^x is 5^x+ln(5)*5^xx