x^-1 * x^-1 =x^(-1 + -1) =x^-2 or alternatively: 1/x times 1/x =1/x^2 (1/x^2) is the same as (x^-2)
By addition. Exponents are multiplied by adding them together. Example: 22 = 4 = (2x2) 23 = 8= (2x2x2) If we multiply 22 x 23 we get (2x2) x (2x2x2) = 4 x 8 = 32 or 22 x 23 = 25 = (2x2) x (2x2x2) = (2x2x2x2x2) = 25 = 32 Same with negative exponents: (A negative exponent indicates a reciprocal (1/x)) 2-2 = 1/4 (1/2 x 1/2) 2-3 = 1/8 (1/2 x 1/2 x 1/2) 2-2 x 2-3 = 1/4 x 1/8 = 1/32 2-2 x 2-3 = (1/2 x 1/2) x (1/2 x 1/2 x 1/2) = (1/2 x 1/2 x 1/2 x 1/2 x 1/2) = 2(-2)+(-3) = 2-5 = 32 Hope this helps.
(x^3 + 2x^2 + 3x - 6)/(x - 1) add and subtract x^2, and write -6 as (- 3) + (-3) = (x^3 - x^2 + x^2 + 2x^2 - 3 + 3x - 3)/(x - 1) = [(x^3 - x^2) + (3x^2 - 3) + (3x - 3)]/(x - 1) = [x^2(x - 1) + 3(x^2 - 1) + 3(x - 1)]/(x - 1) = [x^2(x - 1) + 3(x - 1)(x + 1) + 3(x - 1)]/(x - 1) = [(x - 1)(x^2 + 3x + 3 + 3)]/(x - 1) = x^2 + 3x + 6
x^3 - x^2 + x - 1 = (x^3 - x^2) + (x - 1) = x^2(x - 1) + (x - 1) = (x -1)(x^2 + 1)
Use the chain rule:d/dx √(4 - x) = d/dx (4 - x)1/2= 1/2 (4 - x)-1/2 x d/dx (4 - x)= 1/2 (4 - x)-1/2 x -1= -1/2 (4 - x)-1/2 or -1/2√(4 - x)
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(1+x)/(x^2+1) Let x^2+1 =u 2x dx = du x dx = du/2 (1+x) / (x^2+1) = 1/(x^2+1) + x / (x^2+1) Integral of x dx / (x^2+1) = (1/2) integral du / u = 1/2 ln|u| --(1) Integral of 1 / (x^2+1) = arctan(x) --(2) Adding (1) and (2) Integral (1+x)/(x^2+1) = (1/2) ln(x^2+1) + arctan(x) + C
2/1 x 1/2 = 2 x 1/1 x 2 = 2/2 = 1
x/2 - 12 = 0 x/2 - 1 = 0 Add 1 to both sides of the equation. (x/2)( - 1 + 1) = 0 + 1 x/2 = 1 Multiply both sides of the equation by 2. 2(x/2) = 1 x 2 x = 2
sqrt(x) = x^(1/2) The derivative is (1 / 2) * x^(-1 / 2) = 1 / (2 * x^(1 / 2)) = 1 / (2 * sqrt(x))
(x^3 - 1) = (x - 1)[x^2 + (x)(1) + 1^2] = (x - 1)(x^2 + x + 1)
x^-1 * x^-1 =x^(-1 + -1) =x^-2 or alternatively: 1/x times 1/x =1/x^2 (1/x^2) is the same as (x^-2)
By addition. Exponents are multiplied by adding them together. Example: 22 = 4 = (2x2) 23 = 8= (2x2x2) If we multiply 22 x 23 we get (2x2) x (2x2x2) = 4 x 8 = 32 or 22 x 23 = 25 = (2x2) x (2x2x2) = (2x2x2x2x2) = 25 = 32 Same with negative exponents: (A negative exponent indicates a reciprocal (1/x)) 2-2 = 1/4 (1/2 x 1/2) 2-3 = 1/8 (1/2 x 1/2 x 1/2) 2-2 x 2-3 = 1/4 x 1/8 = 1/32 2-2 x 2-3 = (1/2 x 1/2) x (1/2 x 1/2 x 1/2) = (1/2 x 1/2 x 1/2 x 1/2 x 1/2) = 2(-2)+(-3) = 2-5 = 32 Hope this helps.
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1/2*tan(x)^(1/2)/(cos(x)*sin(x))^(1/2)*cos(x)*2^(1/2)*arccos(cos(x)-sin(x))-1/2*2^(1/2)*ln(cos(x)+2^(1/2)*tan(x)^(1/2)*cos(x)+sin(x))
(x^3 + 2x^2 + 3x - 6)/(x - 1) add and subtract x^2, and write -6 as (- 3) + (-3) = (x^3 - x^2 + x^2 + 2x^2 - 3 + 3x - 3)/(x - 1) = [(x^3 - x^2) + (3x^2 - 3) + (3x - 3)]/(x - 1) = [x^2(x - 1) + 3(x^2 - 1) + 3(x - 1)]/(x - 1) = [x^2(x - 1) + 3(x - 1)(x + 1) + 3(x - 1)]/(x - 1) = [(x - 1)(x^2 + 3x + 3 + 3)]/(x - 1) = x^2 + 3x + 6
x^3 - x^2 + x - 1 = (x^3 - x^2) + (x - 1) = x^2(x - 1) + (x - 1) = (x -1)(x^2 + 1)