-(1/2)X^2 [negative half X squared]
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
anti derivative of ax^n is (a/n+1)x^(n+1) a is a const n is power of variable and answere6x^2
4
It os 1/2*e2x + c
-(1/2)X^2 [negative half X squared]
negative cotangent -- dcot(x)/dx=-csc^2(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
d/dx 2x^2 = 4x
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
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
X/1 is just X. so (1/2)X2 + C or X2/2 + C
the derivative of tangent dy/dx [ tan(u) ]= [sec^(2)u]u' this means that the derivative of tangent of u is secant squared u times the derivative of u.
anti derivative of ax^n is (a/n+1)x^(n+1) a is a const n is power of variable and answere6x^2
4
It os 1/2*e2x + c
It is x|x|/2 + C