You can take out any constant from a derivative. In other words, this is the same as 5 times the derivative of sec x.
f(x)=(pi2)x=pi2x. The derivative of kx=ln(k)*kx, so f'(x)=2ln(pi)*pi2x (with chain rule).
I'm not sure what you're asking. The derivative of 6x is 6. The derivative of x^6 is 6x^5.
The idea is to use the chain rule. Look up the derivative of sec x, and just replace "x" with "5x". Then multiply that with the derivative of 5x.
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
The first derivative of e to the x power is e to the power of x.
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.
You can take out any constant from a derivative. In other words, this is the same as 5 times the derivative of sec x.
2x is the first derivative of x2.
2x is the first derivative of x2.
d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )
The function given is (f(x) = -x^2). The second derivative of a function, denoted as (fâ'(x)), measures the concavity of the function. For the function (f(x) = -x^2), the first derivative (fâ(x)) is (-2x). Taking the derivative of (fâ(x)) gives us the second derivative (fââ(x)), which is (-2). So, (fâ'(x) = -2). This indicates that the function (f(x) = -x^2) is concave down for all (x), because the second derivative is negative.
2x
Use the formula for the derivative of a power. The square root of (x-5) is the same as (x-5)1/2.
f(x)=(pi2)x=pi2x. The derivative of kx=ln(k)*kx, so f'(x)=2ln(pi)*pi2x (with chain rule).
Well if you have 5/X then you can rewrite this like 5x-1. And the derivative to that is -5x-2 and that can be rewrote to: -(5/x2).
y=x^pid/dx=pi*(x^pi-1)This is true because of power rule.d/dx (x^a)=a(x^(a-1))