Find the Derivative of F(x)=4x2(the previous 2 is squared)-2x
y = 4 x^2 -2 x
in general derivative of x^n = n x^(n-1) so
dy/dx = 4 * 2 x^1 - 2 x^0
which is
8 x - 2
Now if you have not had that relation you have to do it from the definition
dy/dx = (y at x+h - y at x) /h as h-->0
here
y at x+h = 4 (x+h)^2 - 2 (x+h)
= 4 x^2 + 8 x h +4 h^2 - 2 x - 2 h
y at x = 4 x^2 - 2 x
difference over h = 8 x + 4 h - 2
as h-->0 that is
8 x - 2
as we already knew
To find the derivative of the function F(x) = 4x^2 - 2x, you can use the power rule of differentiation. The power rule states that for a term of the form x^n, the derivative is given by n*x^(n-1).
Let's apply this rule to each term in F(x) separately:
For the term 4x^2, the power is 2, so we differentiate it as follows:
d/dx (4x^2) = 2 * 4x^(2-1) = 8x
For the term -2x, the power is 1, so we differentiate it as follows:
d/dx (-2x) = 1 * -2x^(1-1) = -2
Now, add the derivatives of each term to get the derivative of the entire function:
F'(x) = 8x - 2
So, the derivative of F(x) = 4x^2 - 2x is F'(x) = 8x - 2.