`f(x) = e^x - x^3` Find the first and second derivatives of the function. Check to see that your answers aer reasonable by comparing the graphs of f, f', and f''

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nees101's profile pic

nees101 | High School Teacher | (Level 2) Adjunct Educator

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Given function is:


Now we will find the first derivative:




The second derivative is obtained by taking the derivative of the first derivative.




Comparison of graphs of f,f' and f'' is shown below:

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a-maths-9's profile pic

a-maths-9 | Middle School Teacher | (Level 1) Adjunct Educator

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now we will find 2nd derivative




hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

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1) If f(x) = e^(nx) ; where n = a real number;

then f'(x) = n*e^(nx)

2) If f(x) = x^n ; where n = a real number

then f'(x) = n*x^(n-1)

Now, given f(x) = (e^x) -  (x^3)

Thus, f'(x) = (e^x) - 3*(x^2)

f"(x) = (e^x) - 6*(x^1) 

or, f"(x) = (e^x) - 6x