If the function is f(x)= 3x^4-5x^2+6, how to find what f'(2) equals to?

Answer 1

The power rule for taking a derivative is:

For f(x) = xⁿ

f '(x) = nx^n-1

And for constants, the derivative is zero.

So for your function: take each piece separately:

1. The derivative of 3x⁴ is (4)3x³ = 12x³
2. The derivative of -5x² is -10x
3. The derivative of 8 is zero

So f '(x) = 12x³ - 10x

So f '(2) = 12(2)³ - 10(2) = 12(8) - 20 = 76