please can you check if this drivative true or not 1-y=1/(1+x)^4 dy/dx=-4/(1+x)^5 2-y=1/(x^2+5x+4)^4 dy/dx=-4/(x^2+5x+4)^5.(2x+5)
What steps can you think of that might let you check them for yourself? 1) You could integrage the results and see if you get what you started with (within an arbitrary constant). 2) You could pick a couple values of x, find the corresponding values of y, and then evaluate the derivatives at those values of x and compare them to the estimates you get from picking a small value of Δx and finding Δy and taking the ratio. 3) Perform some "sanity check" thought experiments. For instance, in the first one, what is the value of y if x is 0? Will this value go up or go down if x is increased by a small amount? Based on this, should the derivative be positive or negative for a small positive value of x? Is the derivative that you derived produce a value that is consistent with this conclusion?