What is the derivative of 6^{2x} ?

The derivative of 6^{2x} is ln(6)*9^x*2^{2x+1}

What is the first derivative of 6^{2x} ?

The first derivative of 6^{2x} is ln(6)*9^x*2^{2x+1}

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\frac{d}{d x} (6^{2 x})

ln (6) \cdot 9^{x} \cdot 2^{2 x + 1}

Solution steps

\frac{d}{d x} (6^{2 x})

Simplify

6^{2 x} : 3 6^{x}

= \frac{d}{d x} (3 6^{x})

Apply the derivative exponent rule:

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

= 3 6^{x} ln (36)

Simplify

3 6^{x} ln (36) : ln (6) \cdot 9^{x} \cdot 2^{2 x + 1}

= ln (6) \cdot 9^{x} \cdot 2^{2 x + 1}

(e^{8 x})^{^{'}}

\frac{d}{d x} (x^{2} - 8, x)

x \to 0 + lim (ln (x) + \frac{1}{x})

\frac{\partial}{\partial x} (\frac{x}{x + 3 y})

\frac{d}{d x} (4 3^{x})

What is the derivative of 6^{2x} ?
The derivative of 6^{2x} is ln(6)*9^x*2^{2x+1}
What is the first derivative of 6^{2x} ?
The first derivative of 6^{2x} is ln(6)*9^x*2^{2x+1}