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

Popular >

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}

\int (e^{- 16 x}) d x

\int t^{2} ln (t) d t

x \to π lim (csc (x + π))

\frac{\partial}{\partial x} (sec^{2} (x y^{2}) y^{2})

\frac{3 s - 5}{( s - 1 ) ^{2}}

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