The antiderivative of x2 + x is 1/3x3 + 1/2x2 + C.
It is x|x|/2 + C
the derivative of ln x = x'/x; the derivative of 1 is 0 so the answer is 500(1/x)+0 = 500/x
-4/x2
13
The anti-derivative of sqrt(x) : sqrt(x)=x^(1/2) The anti-derivative is x^(1/2+1) /(1/2+1) = (2/3) x^(3/2) The anti-derivative is 4e^x is 4 e^x ( I hope you meant e to the power x) The anti-derivative of -sin(x) is cos(x) Adding, the anti-derivative is (2/3) x^(3/2) + 4 e^x + cos(x) + C
The derivative of x divided by 3 is 1/3. This can be found using the power rule of differentiation, where the derivative of x^n is nx^(n-1). In this case, x can be written as x^1, so the derivative is 1(1/3)*x^(1-1) = 1/3.
x (ln x + 1) + Constant
The anti-derivative of 1/x is ln|x| + C, where ln refers to logarithm of x to the base e and |x| refers to the absolute value of x, and C is a constant.
(1/2(x^-1/2))/x
2
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.
anti derivative of ax^n is (a/n+1)x^(n+1) a is a const n is power of variable and answere6x^2
-(1/2)X^2 [negative half X squared]
3
(cos x sin x) / (cos x sin x) = 1. The derivative of a constant, such as 1, is zero.
Negative the derivative of f(x), divided by f(x) squared. -f'(x) / f²(x)