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Math
Calculus
Differentiation Equations
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Terms in this set (7)
Product Rule
y=uv
dy/dx= (u x dv/dx) + (v x du/dx)
Chain rule
y= (2x+x^2)^4
dy/dx= 4(2x+x^2)^3 x (2+2x)
Differentiating sin
d/dx (sin(x)) = cos(x)
d/dx (sin f(x))= f'(x)cos f(x)
Differentiating cos
d/dx (cos(x))= -sin(x)
d/dx (cos f(x))= -f'(x) sin f(x)
Differentiating natural logs
d/dx (ln f(x)) = f'(x)/f(x)
Differentiating e
d/dx (e^f(x)) = f'(x) e^f(x)
Differentiating exponentials
d/dx (a^x) = a^x ln(a)
d/dx (a^kx) = a^kx k ln(a)
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Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a moving car in terms of its speed is $s=1.1 v+0.054 v^{2},$ where s is measured in ft and y in mph. The linear term 1.1v models the distance the car travels during the time the driver perceives a need to stop until the brakes are applied, and the quadratic term $0.054 v^{2}$ models the additional braking distance once they are applied. Find ds/dy at y = 35 and y = 70 mph, and interpret the meaning of the derivative.
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