What is (\partial)/(\partial x)(4^{(x^9)}) ?

The answer to (\partial)/(\partial x)(4^{(x^9)}) is 9ln(2)*2^{2x^9+1}x^8

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(\partial)/(\partial x)(4^{(x^9)})

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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 ^{2}}{d x ^{2}} (4 cos (x))

f (x) = \frac{4}{x ^{5}}

x \to - 2 lim (x^{2} + 5 x)

x \to 2 lim (3 x + 3)

ln (\frac{x - 3}{x + 3})

What is (\partial)/(\partial x)(4^{(x^9)}) ?
The answer to (\partial)/(\partial x)(4^{(x^9)}) is 9ln(2)*2^{2x^9+1}x^8