Find the first and second derivativesy=x2+x+8

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Eve Larson · Accepted Answer

Step 1The derivative of a function at a point is the rate of change of the function with respect to the function variable at that point  which is equal to the slope of the function at that point . The second derivate of a function is the rate of change of the rate of change of the function at the given point w.r.t the function variable . Step 2To determine the first derivative, of the function f(x)=x2+x+8, differentiate the function with respect to x as follows;f(x)=x2+x+8f′(x)=d(f(x))dx=d(x2+x+8)dx=d(x2)dx+d(x)dx+d(8)dx=2*x+1*1+0=2x+1Therefore the first derivative of a function is 2x+1Step 3Now to determine the second derivative, differentiate f&#039;(x) with respect to x again, as follows;f&#039;(x)=2x+1f″(x)=d(f′(x))dx=d(2x+1)dx=d(2x)dx+d(1)dx=2*1+0=2Therefore the second derivative of the function is 2.

Find the first and second derivatives \(\displaystyle{y}={x}^{{{2}}}+{x}+{8}\)

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