What is the derivative of 8^{x^4} ?

The derivative of 8^{x^4} is 3ln(2)*2^{3x^4+2}x^3

What is the first derivative of 8^{x^4} ?

The first derivative of 8^{x^4} is 3ln(2)*2^{3x^4+2}x^3

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\frac{d}{d x} (8^{x^{4}})

3 ln (2) \cdot 2^{3 x^{4} + 2} x^{3}

Solution steps

\frac{d}{d x} (8^{x^{4}})

Apply exponent rule:

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

8^{x^{4}} = e^{x^{4} l n (8)}

= \frac{d}{d x} (e^{x^{4} l n (8)})

Apply the chain rule:

e^{x^{4} l n (8)} \frac{d}{d x} (x^{4} ln (8))

= e^{x^{4} l n (8)} \frac{d}{d x} (x^{4} ln (8))

\frac{d}{d x} (x^{4} ln (8)) = 12 ln (2) x^{3}

= e^{x^{4} l n (8)} \cdot 12 ln (2) x^{3}

Simplify

e^{x^{4} l n (8)} \cdot 12 ln (2) x^{3} : 3 ln (2) \cdot 2^{3 x^{4} + 2} x^{3}

= 3 ln (2) \cdot 2^{3 x^{4} + 2} x^{3}

\frac{x}{1 + x ^{2}}, \frac{x ^{2}}{1 + x ^{3}}, [0, 1]

\int \frac{8}{4 + 8 x} d x

\frac{180}{x ^{7}} - \frac{4}{x ^{3}}

\frac{d y}{d x} = (e^{x} - e^{- x})^{2}

f (x) = x^{2}, (0, - 9)

What is the derivative of 8^{x^4} ?
The derivative of 8^{x^4} is 3ln(2)*2^{3x^4+2}x^3
What is the first derivative of 8^{x^4} ?
The first derivative of 8^{x^4} is 3ln(2)*2^{3x^4+2}x^3