Determine the derivative of y = 2x^2 - 4?

derivative take the number 2 multiply it by the exponent and reduce the exponent by 1 then drop the 4 completely. you have 4x plug your x value of 5 into the new equation and presto your slope is 20rise over 1 run 20/1

f '(x) 4x

f"(5) = 4(5)=20 Slope is 20/1

well.. first things first

dy/dx = 4x

so the gradient or slope of the tangent at the point (5, 46) is to sub. x =5 into the first derivative

the equation can be obtained by using y2-y1=m(x2-x1) .. when you ave already worked out your 'm' the gradient (dy/dx) and you know the two coordinates (5, 46)

Use the power rule for derivatives and the constant rule for derivatives

f(x) = x^p f '(x)= p*x^(p-1) if f(x) = C then dy/dx =y'(x) = 0

In english "bring the power down in front to multiply the term and reduce power by 1", and "constants disappear" when you take their derivative.

Thus y=2x^2 -4

becomes y' = 2*2x^(2-1) + 0 = 4x