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.
The derivative of ex is ex
2x is the first derivative of x2.
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).
x^0 = 1 for all x. The derivative of 1 is always zero.