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Popular >

derivative of 4^{(x^9})

Solution

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

Solution

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}

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Frequently Asked Questions (FAQ)

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