If f(x) = 2x^4, then f'(3) =

To find f'(3) (f prime of 3), you must find f' first.  f' is the derivative of the function f(x).

Finding the derivative of f(x) = 2x⁴ requires the use of the power rule.

The power rule for derivatives is .  In other words, you bring the exponent forward and multiply it by the coefficient of the term, and then you subtract 1 from the original exponent.

f'(x) = (2x⁴)

f'(x) = 2(4)x³

f'(x) = 8x³

Now, to find f'(3), plug 3 into your derivative.

f'(3) = 8(3)³

f'(3) = 216

f'(3) = 216

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.