What is the derivative of 3^{5x} ?

The derivative of 3^{5x} is 5ln(3)*243^x

What is the first derivative of 3^{5x} ?

The first derivative of 3^{5x} is 5ln(3)*243^x

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\frac{d}{d x} (3^{5 x})

5 ln (3) \cdot 24 3^{x}

Solution steps

\frac{d}{d x} (3^{5 x})

Simplify

3^{5 x} : 24 3^{x}

= \frac{d}{d x} (24 3^{x})

Apply the derivative exponent rule:

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

= 24 3^{x} ln (243)

Simplify

ln (243) : 5 ln (3)

= 5 ln (3) \cdot 24 3^{x}

What is the derivative of 3^{5x} ?
The derivative of 3^{5x} is 5ln(3)*243^x
What is the first derivative of 3^{5x} ?
The first derivative of 3^{5x} is 5ln(3)*243^x