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

The derivative of 4^{(x^9)} is 9ln(2)*2^{2x^9+1}x^8

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

The first derivative of 4^{(x^9)} is 9ln(2)*2^{2x^9+1}x^8

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derivative of

4^{(x^{9})}

9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

4^{x^{9}} = e^{x^{9} l n (4)}

= \frac{d}{d x} (e^{x^{9} l n (4)})

Apply the chain rule:

e^{x^{9} l n (4)} \frac{d}{d x} (x^{9} ln (4))

= e^{x^{9} l n (4)} \frac{d}{d x} (x^{9} ln (4))

\frac{d}{d x} (x^{9} ln (4)) = 18 ln (2) x^{8}

= e^{x^{9} l n (4)} \cdot 18 ln (2) x^{8}

Simplify

e^{x^{9} l n (4)} \cdot 18 ln (2) x^{8} : 9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

= 9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

\frac{1}{( 2 + x ) ^{3}}

x \to - \infty lim (3^{- x})

(\frac{11}{6}, - \frac{1}{2}), (\frac{1}{3}, \frac{1}{3})

(1) (3.5)

\int 19 arctan (x) d x

What is the derivative of 4^{(x^9)} ?
The derivative of 4^{(x^9)} is 9ln(2)*2^{2x^9+1}x^8
What is the first derivative of 4^{(x^9)} ?
The first derivative of 4^{(x^9)} is 9ln(2)*2^{2x^9+1}x^8