2x
d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )
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 e to the x power is e to the power of x.
3/(4*square root(x)) ....Mukesh
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.
2x is the first derivative of x2.
d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )
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 e to the x power is e to the power of x.
3/(4*square root(x)) ....Mukesh
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.
2x is the first derivative of x2.
The derivative of ex is ex
It is negative one divided by 4 multiplied by x to the power of 1.5 -1/(4(x^1.5))
-1
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 function given is (f(x) = -x^2). The second derivative of a function, denoted as (f’'(x)), measures the concavity of the function. For the function (f(x) = -x^2), the first derivative (f’(x)) is (-2x). Taking the derivative of (f’(x)) gives us the second derivative (f’‘(x)), which is (-2). So, (f’'(x) = -2). This indicates that the function (f(x) = -x^2) is concave down for all (x), because the second derivative is negative.