What is the derivative of 8^{x^3} ?

The derivative of 8^{x^3} is 9ln(2)*8^{x^3}x^2

What is the first derivative of 8^{x^3} ?

The first derivative of 8^{x^3} is 9ln(2)*8^{x^3}x^2

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\frac{d}{d x} (8^{x^{3}})

9 ln (2) \cdot 8^{x^{3}} x^{2}

Solution steps

\frac{d}{d x} (8^{x^{3}})

Apply exponent rule:

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

8^{x^{3}} = e^{x^{3} l n (8)}

= \frac{d}{d x} (e^{x^{3} l n (8)})

Apply the chain rule:

e^{x^{3} l n (8)} \frac{d}{d x} (x^{3} ln (8))

= e^{x^{3} l n (8)} \frac{d}{d x} (x^{3} ln (8))

\frac{d}{d x} (x^{3} ln (8)) = 9 ln (2) x^{2}

= e^{x^{3} l n (8)} \cdot 9 ln (2) x^{2}

e^{x^{3} l n (8)} = 8^{x^{3}}

= 9 ln (2) \cdot 8^{x^{3}} x^{2}

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\int e^{n x} sin (n x) d x

x \to 0 lim (x sin (\frac{6}{x}))

\frac{d}{d x} (\frac{x}{ln ( 2 x )})

\int 30 t^{5} e^{- t^{6}} d t

What is the derivative of 8^{x^3} ?
The derivative of 8^{x^3} is 9ln(2)*8^{x^3}x^2
What is the first derivative of 8^{x^3} ?
The first derivative of 8^{x^3} is 9ln(2)*8^{x^3}x^2