What is the derivative of x5^{2x} ?

The derivative of x5^{2x} is 2ln(5)*25^xx+25^x

What is the first derivative of x5^{2x} ?

The first derivative of x5^{2x} is 2ln(5)*25^xx+25^x

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

2 ln (5) \cdot 2 5^{x} x + 2 5^{x}

Solution steps

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

Simplify

x \cdot 5^{2 x} : 2 5^{x} x

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

Apply the Product Rule:

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

f = 2 5^{x}, g = x

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

\frac{d}{d x} (2 5^{x}) = 2 ln (5) \cdot 2 5^{x}

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

= 2 ln (5) \cdot 2 5^{x} x + 1 \cdot 2 5^{x}

Simplify

= 2 ln (5) \cdot 2 5^{x} x + 2 5^{x}

What is the derivative of x5^{2x} ?
The derivative of x5^{2x} is 2ln(5)*25^xx+25^x
What is the first derivative of x5^{2x} ?
The first derivative of x5^{2x} is 2ln(5)*25^xx+25^x