(1/2(x^-1/2))/x
Well if you have 5/X then you can rewrite this like 5x-1. And the derivative to that is -5x-2 and that can be rewrote to: -(5/x2).
The anti-derivative of X2 plus X is the same as the anti-derivative of X2 plus the anti-derivative of X. The anti derivative of X2 is X3/3 plus an integration constant C1 The anti derivative of X is X2/2 plus an integration constant C2 So the anti-derivative of X2+X is (X3/3)+(X2/2)+C1+C2 The constants can be combined and the fraction can combined by using a common denominator leaving (2X3/6)+(3X2/6)+C X2/6 can be factored out leaving (X2/6)(2X+3)+C Hope that helps
(X^3-27) divided by (x-3)
xyz/3 Answer 2: You could use the quotient rule in calculus. It would be: 3(D(xyz) - xyz(d(3)/3^2 which produces an answer of 1\3 as the derivative of any constant is 0, and the derivative of any variable with an exponent of 1 is 1.
Following the correct order of operations: derivative of x^2 + 6/2 = derivative of x^2 +3, which equals 2x
the derivative of 3x is 3 the derivative of x cubed is 3 times x squared
d/dx of 6*x^(-1/3) = (-6/3)*x^(-4/3) = -2*x^(-4/3), by power rule
1 divided by x to the third power equals x to the negative third. The derivative of x to the negative third is minus three x to the negative fourth.
-4/x2
Negative the derivative of f(x), divided by f(x) squared. -f'(x) / f²(x)
x4/12 since derivative of x4/12 is 4x3/12 or x3/3
m
10/x3 = 10 x-3d/dx(10x-3) = -30 x-4 = -30/x4
The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).
Oh, dude, the third derivative of ln(x) is -2/(x^3). But like, who really needs to know that, right? I mean, unless you're planning on impressing your calculus teacher or something. Just remember, math is like a puzzle, except no one actually wants to put it together.
if y=7/(x^3)-4/xthenby the quotient ruley'=(((0)(x^3)-(7(3x^2))/((x^3)^2))-(((0x)-(4))/(x^2))