Differentiate y = x5√x. SOLUTION Since both the base and the exponent are variable, we use logarithmic differentiation: ln y = ln x5√x = 5 x ln(x) y' y = 5 x · + (ln(x)) · y' = y + 5 ln(x) = x5√x . Another method is to write x5√x = eln(x) 5√x : d dx x5√x = d dx = d dx 5 x ln(x) = x5√x .

Stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height, h(t), in meters (as it relates to sea level), of the sunglasses after t seconds, is shown in the table. during its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. to the nearest meter, what is difference in elevation between stefano and the climber? 166 meters 176 meters 230 meters 240 meters its b.176 i took the test 166 is wrong and 176 is correct