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y = x^5 + x^3 + x^2 + x
y' = 5x^(5 - 1) + 3x^(3 - 1) + 2x^(2 -1) + 1x^(1 - 1) (note x^1 = x and x^0 = 1)
y' = 5x^4 + 3x^2 + 2x + 1
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What is the anti derivative of x squared plus x?
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
What is the derivative of ln x divided by x cubed?
I will use the quotient rule here. d/dx(f(x)/g(x) = g(x)*f'(x) - f(x)*g'(x)/[g(x)]2 x3*1/x - ln(x)*3x2/(x3)2 x3/x - 3ln(x)x2/x6 x2 - 3ln(x)x2/x6 = - 3ln(x)/x4 =========
How do you factor x3 plus 1?
x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - x + 1)
Factor x3 plus 8?
x3 + 8 = x3 + 23 = (x + 2)[x2 - (x)(2) + 22] = (x + 2) (x2 - 2x + 4)
The cube of a number equals the square of the same number find the number?
x3=x2 x3-x2=0 Factor out x2 x2(x - 1) = 0 If x2=0 then x=0. If x - 1 = 0 then x = 1. Therefore the number is 0 or 1.
What is the anti derivative of x squared plus x?
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
What is the anti-derivative of x squared plus 3?
∫ (x2+3) = ∫x2 + ∫3(1/3)X3 + 3X + C
How do you factor x3?
X3 X(X2) X2(X) and, X * X * X
What is the derivative of ln x divided by x cubed?
I will use the quotient rule here. d/dx(f(x)/g(x) = g(x)*f'(x) - f(x)*g'(x)/[g(x)]2 x3*1/x - ln(x)*3x2/(x3)2 x3/x - 3ln(x)x2/x6 x2 - 3ln(x)x2/x6 = - 3ln(x)/x4 =========
What is x3-x2-x minus 2 factored?
x3-x2
What is a grouping factor for polynomial x3 ax 3a 3x2?
x3 + ax + 3a + 3x2 = x (x2 + a) + 3 (a + x2) = x (x2 + a) + 3 (x2 + a) = (x2 + a)(x + 3) Checking the work: x3 + ax + 3x2 + 3a or x3 + 3x2 + 3a + ax = x2 (x + 3) + a (3 + x) = x2 (x + 3) + a (x + 3) = (x + 3)(x2 + a)
How do you factor x3-x2?
Answer: x (x2-x)
How do you factor x3 plus 1?
x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - x + 1)
What is x3 - x2 plus x - 2 factored?
x3 - x2 + x - 2 has no rational factors.
How do you factor x3 plus x2-3x-3?
x3 + x2 - 3x - 3 x(x2 + x - 3) - 3
What is x3-x2 plus 2x factored?
x3 - x2 + 2x = x*(x2 - x + 2) which cannot be factored further.
What is the derivative and second derivative of lnx to the third power?
If you mean: y =(lnx)3 then: dy/dx = [3(lnx)2]/x ddy/dx = [(6lnx / x) - 3(lnx)2] / x2 If you mean: y = ln(x3) Then: dy/dx = 3x2/x3 = 3/x = 3x-1 ddy/dx = -3x-2 = -3/x2
