Find the first and second derivatives y=x2+x+8

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Find the first and second derivatives  y=x2+x+8

gwibdaithq · Accepted Answer

Step 1The derivative of a function at a point is the slope of the function at that point divided by the rate of change of the function with respect to the function variable at that point. The rate of change of the rate of change of the function at the given moment w.r.t. the function variable is a function&#039;s second derivate.Step 2To calculate the function&#039;s first derivative&amp;nbsp;f(x)=x2+x+8, the function should be differentiated in relation to x as follows:f(x)=x2+x+8f′(x)=d(f(x))&amp;nbsp;dx&amp;nbsp;=d(x2+x+8)&amp;nbsp;dx&amp;nbsp;=d(x2)&amp;nbsp;dx&amp;nbsp;+d(x)&amp;nbsp;dx&amp;nbsp;+d(8)&amp;nbsp;dx&amp;nbsp;=2*x+1*1+0=2x+1Consequently, a function&#039;s initial derivative is 2x+1.Step 3Now, differentiate f&#039;(x) with regard to x once more to obtain the second derivative as follows:f&#039;(x)=2x+1f&amp;nbsp;″(x)=d(f′(x))&amp;nbsp;dx&amp;nbsp;=d(2x+1)&amp;nbsp;dx&amp;nbsp;=d(2x)&amp;nbsp;dx&amp;nbsp;+d(1)&amp;nbsp;dx&amp;nbsp;=2*1+0=2As a result, the function&#039;s second derivative is 2.

Find the first and second derivatives y=x^{2}+x+8

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