What is the derivative of 2^{5x} ?

The derivative of 2^{5x} is 5ln(2)*32^x

What is the first derivative of 2^{5x} ?

The first derivative of 2^{5x} is 5ln(2)*32^x

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

5 ln (2) \cdot 3 2^{x}

Solution steps

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

Simplify

2^{5 x} : 3 2^{x}

= \frac{d}{d x} (3 2^{x})

Apply the derivative exponent rule:

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

= 3 2^{x} ln (32)

Simplify

ln (32) : 5 ln (2)

= 5 ln (2) \cdot 3 2^{x}

What is the derivative of 2^{5x} ?
The derivative of 2^{5x} is 5ln(2)*32^x
What is the first derivative of 2^{5x} ?
The first derivative of 2^{5x} is 5ln(2)*32^x