The rule for differentiation for variable with exponents has the formula:

d/dx (xⁿ) = nxⁿ⁻¹
where n is the exponent

Thus, for the given equation, the solution is as follows:
y = 2x²
dy/dx = 2(2)x²⁻¹ = <em>4x

Thus, the derived equation of the given would now be 4x.</em>

3 0

2 years ago

Help please: A bus and a train leave a station at the same time, t = 0. The graph shows the bus's distance to the next station o

Nonamiya [84]

Answer:

y = (5/2)x + 20

Step-by-step explanation:

Since the bus and train are both at the station at time 0, the y-intercept for the new equation is 20. That is one point on the new graph: (0,20) The question said that the train travels faster, that means it spends less time getting to the next station. The existing graph shows the bus got to the next station in 10 minutes, so maybe the train got there in 8 minutes. So another point on the graph is (8,0) We can use a slope formula to calculate the slope of a new line. Or just count squares on the graph (se image) to find the slope. Slope tells how steep a line is, whether the line is going up or down, but also the slope is like directions how to get from one point to another point on the line.

All you need to write an equation is the slope, m and the y-intercept, b and fill those two numbers into the formula y=mx+b Here slope is 5/2 and y-intercept is 20. So you get

y=(5/2)x +20