Find the first and second derivatives. y=\frac{x^{3}}{3}+\frac{x^{2}}{2}+e^{-x}

jernplate8

jernplate8

Answered question

2021-06-08

Find the first and second derivatives.
y=x33+x22+ex

Answer & Explanation

timbalemX

timbalemX

Skilled2021-06-09Added 108 answers

Step 1
Given:
y=x33+x22+ex
Step 2
Calculation:
To find the first derivative, we have to differentiate the function with respect to x.
dydx=3x23+2x2+(ex),(Using power rule: ddx(xa)=axa1)
dydx=x2+xex...(1)
Step 3
To find the second derivative, we have to differentiate the equation (1) with respect to x.
d2ydx2=2x+1(ex),(Using power rule: ddx(xa)=axa1)
d2ydx2=2x+1+ex...(2)
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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