Derivative rule

Question

Suppose that f(x)=2x^-4+9x^-2

Evaluate f '(2)=

f '(-2)=

PLEASE HELP

Answer 1

f'(x) = -8x^-5 -18x^-3

f'(-2) = -8/-2^5 - 18/-2^3 = 8/32 + 18/8 = 1/4 + 9/4 = 10/4 = 5/2

f'(-2) = 5/2 = 2.5

f'(2) = -8/2^5 -18/2^3 = -2.5

f'(2) = -f(-2)

f(-2) = -f(2)

take the exponent and multiply it by the coefficient, then reduce the exponent by 1.

-4 times 2 = -8. -4-1 = -5.

-2 times 9 = -18. -2-1 = -3

2^5 = 32

2^3 =8

if the exponent is negative, put the term in the denominator and change the sign to positive.

2^-5 = 1/2^5

2^-3 = 1/2^3