What is the derivative of 5^xln(5) ?

The derivative of 5^xln(5) is ln^2(5)*5^x

What is the first derivative of 5^xln(5) ?

The first derivative of 5^xln(5) is ln^2(5)*5^x

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derivative of

5^{x} ln (5)

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the derivative exponent rule:

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

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

Simplify

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

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

What is the derivative of 5^xln(5) ?
The derivative of 5^xln(5) is ln^2(5)*5^x
What is the first derivative of 5^xln(5) ?
The first derivative of 5^xln(5) is ln^2(5)*5^x