What is the derivative of (4^x)^9 ?

The derivative of (4^x)^9 is 9ln(2)*2^{18x+1}

What is the first derivative of (4^x)^9 ?

The first derivative of (4^x)^9 is 9ln(2)*2^{18x+1}

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derivative of

(4^{x})^{9}

9 ln (2) \cdot 2^{18 x + 1}

Solution steps

\frac{d}{d x} ((4^{x})^{9})

Simplify

(4^{x})^{9} : 26214 4^{x}

= \frac{d}{d x} (26214 4^{x})

Apply the derivative exponent rule:

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

= 26214 4^{x} ln (262144)

Simplify

26214 4^{x} ln (262144) : 9 ln (2) \cdot 2^{18 x + 1}

= 9 ln (2) \cdot 2^{18 x + 1}

\frac{d y}{d x}, 4^{x} = 2 x y

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What is the derivative of (4^x)^9 ?
The derivative of (4^x)^9 is 9ln(2)*2^{18x+1}
What is the first derivative of (4^x)^9 ?
The first derivative of (4^x)^9 is 9ln(2)*2^{18x+1}