What is the derivative of 5^{6x} ?

The derivative of 5^{6x} is 6ln(5)*15625^x

What is the first derivative of 5^{6x} ?

The first derivative of 5^{6x} is 6ln(5)*15625^x

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derivative of

5^{6 x}

6 ln (5) \cdot 1562 5^{x}

Solution steps

\frac{d}{d x} (5^{6 x})

Simplify

5^{6 x} : 1562 5^{x}

= \frac{d}{d x} (1562 5^{x})

Apply the derivative exponent rule:

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

= 1562 5^{x} ln (15625)

Simplify

ln (15625) : 6 ln (5)

= 6 ln (5) \cdot 1562 5^{x}

What is the derivative of 5^{6x} ?
The derivative of 5^{6x} is 6ln(5)*15625^x
What is the first derivative of 5^{6x} ?
The first derivative of 5^{6x} is 6ln(5)*15625^x