Higher-Order Derivatives f(x)=2x^{4}-3x^{3}+2x^{2}+x+4 find f^{10}(x) =

chezmarylou1i

chezmarylou1i

Answered question

2022-01-14

Higher-Order Derivatives
f(x)=2x43x3+2x2+x+4
find f10(x)=

Answer & Explanation

censoratojk

censoratojk

Beginner2022-01-15Added 46 answers

Step 1
We will apply the power rule to find the derivatives.
We find f1(x) first
f(x)=2x43x3+2x2+x+4
f1(x)=2(4x3)3(3x2)+2(2x)+1
f1(x)=8x39x2+4x+1
Step 2
Then we differentiate f1(x) to get f2(x)
f1(x)=8x39x2+4x+1
f2(x)=8(3x2)9(2x)+4
f2(x)=24x218x+4
Then we differentiate f2(x) to get f3(x)
f2(x)=24x218x+4
f3(x)=24(2x)18(1)
f3(x)=48x18
Then we differentiate f3(x) to get f4(x)
f3(x)=48x18
f4(x)=48(1)
f4(x)=48
Then we differentiate f4(x) to get f5(x)
f4(x)=48
f5(x)=0
Since the 5th order derivative is 0, so the other higher-order derivatives will be 0 too.
Answer: f10(x)=0

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