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

the answer is:

the lateral area is equal to

to find the lateral area of the square pyramid, first we need to find the perimeter of the base, and then, find the lateral area using the following formulas:

where,

s, is the base length

slant height, is the height of a the side of the pyramid

we are given:

now, calculating the perimeter of the base, we have:

then, calculating the lateral area:

hence, we have that the lateral area is equal to

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