The outside function is #cos x#, which has a derivative of #-sin x# The inside function is #sin 2x#. For the inside function, the chain rule can be used again. The outside is #sin x# and the inside is #2x# . …

The absolute value function does not have an inverse function. In order for a function f to have an inverse function, f cannot give the same values for two different domain values. (You can't get the …

Dec 2, 2017 · The velocity function is #v (t)=t^2−4t+3# for a particle moving along a line. Find the displacement (net distance covered) of the particle during the time interval # [−1,6]#. Calculus

Explanation: We need #a^2-b^2= (a+b) (a-b)# Let's rewrite the function by factorising # (x^2-1)/ (2-3x)= ( (x+1) (x-1))/ (2-3x)# Let #f (x)= ( (x+1) (x-1))/ (2-3x ...

The slope of a function's tangent line at a point is given by the function's derivative. So, we need to find the derivative of √x − 5 = (x −5)1 2. Note that d dx x1 2 = 1 2 x− 1 2. So, the chain rule states that if …

"R": {y inRR | y = -5} The range of a function in general, is a set of all possible values as the y-coordinate. By graphing (or simply looking) y=-5, we see that y is only -5, no matter the x-value. (It's …

When you graph this, the graph of the function will be symmetric in respect to the y- axis. If f (x)!=f (-x), you could check whether f (-x) equals -f (x). If it does, than the function is odd. If it doesn't, then the …

1 Answer Alan P. May 21, 2015 A function, #f (x)# is discontinuous at a point #x=hatx# if

From b. f' (x)=1 Now f' (2) means first derivative of function f (x) at x=2. Since first derivative has been found to be constant=1, therefore it is independent of the value of x.

This agrees algebraically if we are interested in minimizing the residual difference, usually using sum of squared loss function eg #f_beta= (y-xbeta)^2# #fprime_beta=-2x (y-xbeta)=0# #=2x^2beta=2xy# …