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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\frac{d}{d x} ((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{\partial}{\partial y} (5 x^{\frac{4}{5}} y^{\frac{1}{5}})

\int cos^{2} (t) + sin^{2} (t) d t

\frac{\partial}{\partial z} (8 y arctan (\frac{x}{z}))

x \to 8 lim (5 x - 2)

\frac{d}{d x} (A x e^{\frac{x}{2}} + B)

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}