What is the derivative of (5^x/(ln(5))) ?

The derivative of (5^x/(ln(5))) is 5^x

What is the first derivative of (5^x/(ln(5))) ?

The first derivative of (5^x/(ln(5))) is 5^x

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

5^{x}

Solution steps

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

Take the constant out:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (5^{x})

Apply the derivative exponent rule:

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

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

Simplify

\frac{1}{ln ( 5 )} \cdot 5^{x} ln (5) : 5^{x}

= 5^{x}

\int (e - x - e^{2}) (e x + e - 5) d x

\int 3 e^{3 x} d x

\frac{d}{d x} (\frac{3}{x + 3})

2 x - 3 y x^{2} + 1 \frac{d y}{d x} = 0

\int sinh (ln (x)) d x

What is the derivative of (5^x/(ln(5))) ?
The derivative of (5^x/(ln(5))) is 5^x
What is the first derivative of (5^x/(ln(5))) ?
The first derivative of (5^x/(ln(5))) is 5^x