use the double angle formula for cos(2x) which is: cos(2x)=2cos^2(x)-1 by this relation cos^2(x)=(cos(2x)+1)/2 now we'd integrate this instead this will give sin(2x)/4+x/2 =) hope this helps
Differentiating x^2 can be accomplished by using the Power Rule. This provides that d/dx (x^2)=2x
2x+x is 3x
(2x + 1) + (x*x - 2x + 1) = x^2 + 2x - 2x + 1 + 1 = x^2 + 2
2X * 2X * 2X = 8X^3 2X^3 is saying 2*( X * X * X) = 2X^3
The derivative with respect to x of any term in this format: axn is equal to: nax(n -1) so in the case of x2, the answer will be: 2x(2 - 1) = 2x1 = 2x
cos x
The answer is ln(2)2x where ln(2) is the natural log of 2. The answer is NOT f(x) = x times 2 to the power(x-1). That rule applies only when the exponent is a constant.
d/dx(cos x) = -sinx
0
d/dx(2x) = 2 simple power rule
Differentiate term by term. d/dx[X2 + 2X) = 2X + 2 slope(m) = 2 ------------------
If you actually mean "... with respect to x", and that y is equal to this function of x, then the answer is:y = x sin(x)∴ dy/dx = sin(x) + x cos(x)
use the double angle formula for cos(2x) which is: cos(2x)=2cos^2(x)-1 by this relation cos^2(x)=(cos(2x)+1)/2 now we'd integrate this instead this will give sin(2x)/4+x/2 =) hope this helps
Differentiating x^2 can be accomplished by using the Power Rule. This provides that d/dx (x^2)=2x
x = yy differentiate both sides with respect to x dx = (y * yy-1) dy dy/dx = y * yy-1 dy/dx = yy = x hence differentiate of y wrt x is x only
1/2x