Find the first and second derivatives of the given function. f(x)=5x^{3}-6x^{2}+6

Krzychau1 2021-12-16 Answered
Find the first and second derivatives of the given function.
f(x)=5x36x2+6
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Expert Answer

Kayla Kline
Answered 2021-12-17 Author has 37 answers
Step 1
The given function is f(x)=5x36x2+6.
The derivative of xn is given by: ddx(xn)=nxn1
and derivative of constant is zero, that is ddx(c)=0.
Step 2
To find the first derivative of the given function f(x)=5x36x2+6, differentiate this function with respect to x.
f(x)=5x36x2+6
f(x)=ddx(6x36x2+6) (since, ddxf(x)=f(x))
f(x)=ddx(5x3)+ddx(6x2)+ddx(6)
f(x)=5ddx(x3)6ddx(x2)+ddx(6)
f(x)=5(3x(31))6(2x(21))+0
f(x)=15x212x
Therefore, first derivative of the given function is f(x)=15x212x.
Step 3
To find second derivative of the given function, differentiate first derivative f(x)=15x212x with respect to x.
f(x)=ddx(15x212x) (since, d2dx2f(x)=f(x))
chumants6g
Answered 2021-12-18 Author has 33 answers
d2dx2(5x36x2+6)
ddx(5x36x2+6)=15x212x
=ddx(15x212x)
ddx(15x212x)=30x12
=30x-12

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