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Popular >

derivative of 8^{x^8}

Solution

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

Solution

3 ln (2) \cdot 2^{3 x^{8} + 3} x^{7}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{8} ln (8)) = 24 ln (2) x^{7}

= e^{x^{8} l n (8)} \cdot 24 ln (2) x^{7}

Simplify

e^{x^{8} l n (8)} \cdot 24 ln (2) x^{7} : 3 ln (2) \cdot 2^{3 x^{8} + 3} x^{7}

= 3 ln (2) \cdot 2^{3 x^{8} + 3} x^{7}

Popular Examples

integral of (2/(sqrt(x))+2sqrt(x))

\int (\frac{2}{x} + 2 x) d x

(\partial)/(\partial x)((2x^2)/(y^2+x^2))

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

integral from-1 to 1 of (2/(x^2+1))

\int_{- 1}^{1} (\frac{2}{x ^{2} + 1}) d x

integral of e^{-0.4x}

\int e^{- 0.4 x} d x

limit as x approaches-2 of (x+2)/(x^3+8)

x \to - 2 lim (\frac{x + 2}{x ^{3} + 8})

Frequently Asked Questions (FAQ)

What is the derivative of 8^{x^8} ?
The derivative of 8^{x^8} is 3ln(2)*2^{3x^8+3}x^7
What is the first derivative of 8^{x^8} ?
The first derivative of 8^{x^8} is 3ln(2)*2^{3x^8+3}x^7