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The formula for the derivative of an inverse
(finv)' = 1/(f' o (finv))
allows you get a formula for the derivative of the inverse of any function that you already know the derivative of.
For example: What is the derivative of sqrt(x)? You could figure this out using the definition of the derivative, but it is complicated. You already know that the derivative of x2 is 2x. So let f = x2; finv = sqrt(x), f' = 2x. This gives:
(sqrt(x))' = 1/(2 sqrt(x)).
Now you have derived a "square root rule" with almost no work.
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What is an antiderivative?
It is an inverse function of a derivative, also known as an integral.
What is the Derivative of the inverse sin of X?
1/(1-x2 )1/2
Differentiate inverse function from logarithmic function?
The inverse of the natural log function lnx is exA function must be one to one to have an inverse and the log function is.I am not sure if that is what you are asking.The derivative of ex is itself.That is to say if f(x)=ex then f'(x)=exIf you are asking about the derivative of lnx, it is 1/xand if you look at logb x=1/(xlnb)Not sure which one you are looking for.
What is the chain rule in calculus?
The chain rule, in calculus, is a formula. It allows one to compute the derivative of the composition of two or more functions. It was first used by the German mathematician Gottfried Leibniz.
Proof of the derivative of the cosecant function?
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).
