What is the derivative of 5^{mx} ?

The derivative of 5^{mx} is ln(5)*5^{mx}m

What is the first derivative of 5^{mx} ?

The first derivative of 5^{mx} is ln(5)*5^{mx}m

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

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{m x} = e^{m x l n (5)}

= \frac{d}{d x} (e^{m x l n (5)})

Apply the chain rule:

e^{m x l n (5)} \frac{d}{d x} (m x ln (5))

= e^{m x l n (5)} \frac{d}{d x} (m x ln (5))

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

= e^{m x l n (5)} ln (5) m

e^{m x l n (5)} = 5^{m x}

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

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What is the derivative of 5^{mx} ?
The derivative of 5^{mx} is ln(5)*5^{mx}m
What is the first derivative of 5^{mx} ?
The first derivative of 5^{mx} is ln(5)*5^{mx}m