Question

differentiate 8 to the power x divided by x to the power 8​

Answer 1

Answer:

$\frac{dy}{dx} = \frac{ {8}^{x} }{ {x}^{8} } ( ln(8) - \frac{8}{x} )$

Step-by-step explanation:

y = 8^x / x^8

y x^8 = 8^x

y' x^8 + y 8x^7 = ln(8) 8^x

y' x^8 + ( 8^x / x^8 ) 8x^7 = ln(8) 8^x

y' x^8 + 8^(x+1)/x = ln(8) 8^x

y' x^8 = 8^x( ln(8) - 8/x )

$\frac{dy}{dx} = \frac{ {8}^{x} }{ {x}^{8} } ( ln(8) - \frac{8}{x} )$