(x23)'=23x22 Generally, (xn)'=n*xn-1
The derivative of sin(x) is cos(x).
if f(x)=kx, f'(x)=ln(k)*kx. Therefore, the derivative of 2x is ln(2)*2x.
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
The derivative of sec(x) is sec(x) tan(x).
To differentiate y=sin(sin(x)) you need to use the chain rule. A common way to remember the chain rule is "derivative of the outside, keep the inside, derivative of the inside". First, you take the derivative of the outside. The derivative of sin is cos. Then, you keep the inside, so you keep sin(x). Then, you multiple by the derivative of the inside. Again, the derivative of sinx is cosx. In the end, you get y'=cos(sin(x))cos(x))
The first derivative of e to the x power is e to the power of x.
2x is the first derivative of x2.
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
The first derivative of ln x is 1/x, which (for the following) you better write as x-1.Now use the power rule:Second derivative (the derivative of the first derivative) is -1x-2, the third derivative is the derivative of this, or 2x-3. You may now wish to write this in the alternative form, as 2 / x3.
d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )
The derivative of ex is ex
x^0 = 1 for all x. The derivative of 1 is always zero.
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
2x
Express the cosecant in terms of sines and cosines; in this case, csc x = 1 / sin x. This can also be written as (sin x)-1. Remember that the derivative of sin x is cos x, and use either the formula for the derivative of a quotient (using the first expression), or the formula for the derivative of a power (using the second expression).
the derivative of 1x would be 1 the derivative of x to the power of 1 would be 1. the derivative of x+1 would be 1 the derivative of x-1 would be 1 im not sure what you are asking, but however you put it, it's 1.