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

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

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

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

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derivative of

f (x) = 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{d}{d x} (lo g_{e} (x))

\int \frac{9}{x ^{2} x ^{2} + 16} d x

tan^{2} (5 θ)

n = 1 \sum \infty 5 (- 1)^{n} n x^{n}

e^{- 4}

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