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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).
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
What is the derivative of inverse tangent of x?
d/dx[ tan-1(x) ] = 1/(1 + x2)
How are derivatives and anti derivatives related?
The derivative is the inverse of the integral. ∫ f'(x) dx = f(x) + C
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.
What is the formula of inverse of function?
f=by+xbygf*yt -gkft
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).
What is the second derivitive of sec 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.
What is the derivative of square root of x-5?
Use the formula for the derivative of a power. The square root of (x-5) is the same as (x-5)1/2.
What is an inverse formula?
It is a formula that is the reverse of another one.I.e if you put x = 1 into a formula and get y = 5, with the inverse formula you would put x =5 and get y = 1.To work out an inverse I will give an example:Y = 2X + 7there are 2 ways to do it, but my favourite is to replace ys with xs and vice versa so:X = 2Y + 7rearrange to get it as Y =...2Y = X - 7Y = (X-7)/2 Now put in a number like x = 5 into the top equation and you get y = 17 then putting x = 17 into the bottom equation you get 5, which means it is correct, the inverse.
What is the derivative of inverse hyperbolic function?
For example. d/dx sin^-1 X = 1/sqrt(1 - x^2) Probably derived from the Pythagorean theorem.
