Higher-Order Derivatives f(x)=2x4−3x3+2x2+x+4 find f10(x)=?

Question

Higher-Order Derivatives  f(x)=2x4−3x3+2x2+x+4  find f10(x)=?

Aubree Mcintyre · Accepted Answer

We will apply the power rule to find the derivatives.
We find

f^{1} (x)

first

f (x) = 2 x^{4} - 3 x^{3} + 2 x^{2} + x + 4

f^{1} (x) = 2 (4 x^{3}) - 3 (3 x^{2}) + 2 (2 x) + 1

f^{1} (x) = 8 x^{3} - 9 x^{2} + 4 x + 1

Step 2
Then we differentiate

f^{1} (x) \to \geq t f^{2} (x)

f^{1} (x) = 8 x^{3} - 9 x^{2} + 4 x + 1

f^{2} (x) = 8 (3 x^{2}) - 9 (2 x) + 4

f^{2} (x) = 24 x^{2} - 18 x + 4

Then we differentiate

f^{2} (x) \to \geq t f^{3} (x)

f^{2} (x) = 24 x^{2} - 18 x + 4

f^{3} (x) = 24 (2 x) - 18 (1)

f^{3} (x) = 48 x - 18

Then we differentiate

f^{3} (x) \to \geq t f^{4} (x)

f^{3} (x) = 48 x - 18

f^{4} (x) = 48 (1)

f^{4} (x) = 48

Then we differentiate

f^{4} (x) \to \geq t f^{5} (x)

f^{4} (x) = 48

f^{5} (x) = 0

Since the 5th order derivative is 0, so the other higher-order derivatives will be 0 too.
Result:

f^{10} (x) = 0

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