the derivative from scribit that means holy writing is scripture
The derivative of 2x2 + 4x + 8 is 4x+4.
x = 10x, so derivative = 10
2
4x
9x2
y"+y'=0 is a differential equation and mean the first derivative plus the second derivative =0.Look at e-x the first derivative is -e-xThe second derivative will be e-xThe sum will be 0
y is a sum of constants and so is itself a constant. Its derivative is, therefore, zero.
negative sin(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 of lnx is 1/x Therefore the derivative is 1/(1+x)
Following the correct order of operations: derivative of x^2 + 6/2 = derivative of x^2 +3, which equals 2x
the derivative of ln x = x'/x; the derivative of 1 is 0 so the answer is 500(1/x)+0 = 500/x