Find the derivative of the function below by simplifying So we can take logs of both sides to find How do you solve 2x2 + x + 7 = 0
Algebra quadratic equations and functions comparing methods for solving quadratics Then log(y) is well defined How do you find the derivative of f (x) = x2 − 4x + 3
(1 x)3 = 1 ⋅ 1 ⋅ 1 x ⋅ x ⋅ x recall that x ⋅ x ⋅ x = x3 (1 x)3 = 1 x3 we can also use the rule (a b)n = an bn to show that (1 x)3 = 13 x3 = 1 x3 this can be rewritten, but whether or not it is a simplification is up for debate We can use a negative exponent, since a−b = 1 ab to show that 1 x3 = x−3 answer link #differentiate using the color (blue)product rule# #given f (x)=g (x)h (x) then# #f' (x)=g (x)h' (x)+h (x)g' (x)larrcolor (blue)product rule# #g (x)=6x^2rarrg' (x)=12x#
#h (x)=ln4xrarrh' (x)=1/ (4x)xxd/dx (4x)=1/ (4x) xx4=1/x# See the entire solution process below First, expand the terms in parenthesis 8x + 4 = 8x + 4 because each side of the equation is exactly the same we know x can be any value and this equation will be true
Drawing a right triangle with an angle y such that tan(y) = x − 1, we can find that sec(y) = √x2 − 2x + 2 Plugging that in, we get our result D dx arctan(x − 1) = 1 x2 − 2x +2 note that the same process shows that the formula for d dx arctan(x) = 1 x2 + 1 If we already have that formula, then we can simply use the chain rule:
What is the vertex form of y = x2 + 9x − 22? So the range is (0, oo) or a subset of it
