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

Efan Halliday 2020-10-27 Answered
Higher-Order Derivatives
f(x)=2x43x3+2x2+x+4
find f10(x)=?
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Expert Answer

Aubree Mcintyre
Answered 2020-10-28 Author has 73 answers
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)tf2(x)
f1(x)=8x39x2+4x+1
f2(x)=8(3x2)9(2x)+4
f2(x)=24x218x+4
Then we differentiate f2(x)tf3(x)
f2(x)=24x218x+4
f3(x)=24(2x)18(1)
f3(x)=48x18
Then we differentiate f3(x)tf4(x)
f3(x)=48x18
f4(x)=48(1)
f4(x)=48
Then we differentiate f4(x)tf5(x)
f4(x)=48
f5(x)=0
Since the 5th order derivative is 0, so the other higher-order derivatives will be 0 too.
Result: f10(x)=0
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