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Derivative to Related Rates Transition?
In the first quarter of the year my class studied derivatives and found that the derivative of
for example x^2= 2x
now we are studying related rates and my teacher also puts on a dx/dt after the 2x can somebody explain when to put on dx/dt and when not to?
2 Answers
- ?Lv 41 decade agoFavorite Answer
The derivative of x^2 can also be written as: 2x d/dx
Now say you introduce another variable:
y = x^2 ||| the derivative could be written as y' = 2x * dx/dy
You are now taking the derivative of x in relation to y ("dx/dy")
You can differentiate different variables with respect to another variable, and in your case... x is being differentiated with respect to y.
If your function was F(x) or t = x^2; then you can figure out the differential with respect to "t"
= 2x dx/dt
- ?Lv 44 years ago
enable s be the dimensions of a facet. Then, A = s^2. be conscious that once A = sixteen sq. cm, then s = sqrt(sixteen) = 4 cm. Differentiating the two factors with comprehend to t provides dA/dt = 2s ds/dt. (remember that the two s and a metamorphosis with time t!!) enable s = 4 cm and ds/dt = 6 cm/sec. (The expenditures have the extra complicated instruments.) So, dA/dt = 2* 4 *6 = 40 8 sq. cm/ 2d.