Use logarithmic differentiation to find the derivative of the function. y = x8 cos(x)

the derivative is   dy/dx = 8x⁷ cos(x) - x⁸ sin(x)  

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take the natural logarithm of both sides

use log law ln(xy) = ln(x) + ln(y) to expand

implicitly differentiate both sides with respect to x.

use chain rule.

since y = x⁸ cos(x), we substitute that in so we get dy/dx in terms of x

is should be y = 5x

step-by-step explanation:

correct me if im wrong

a. 12.5 kg

step-by-step explanation:

f = ma

so

m = f/a = (2500 n)/(200 m/s²) = 12.5 kg

1 n = 1 kg·m/s²