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what is differentiation for?

When differentiating you find the gradient of the function/line, this means how fast does the function goes up or down.
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Answered by Richard B. • Maths tutor
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Differentiate: y=x^x

First take log’s each side as it would turn our complicated function into something differentiable by chain rule. ln y = x*ln x Then differentiate y with respect to x: d(ln y)/dx = ln x + 1 1/y * dy/dx = ln ...
MV
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Differentiate: ln((e^x+1)/e^x-1))

Chain rule: First resolve the log differential, then resolve the fraction integration either by knowing the formula for it or by writing (e^x+1)/(e^x-1) as (e^x+1)(e^x-1)^(-1) and applying chain rule againLe...
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Answered by Mihai V. • Maths tutor
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A machine is used to manufacture custom spoilers for two types of sports car( Car A and Car B0. Each day, in a random order, n are produced for Car A and m for Car B. What is the probability that the m spoilers for Car B are produced consecutively?

First we look at the probability of producing a total ensemble which is 1/(n+m)!. This is in any random order and any part either m or n To further see what is going on let’s take some example let’s have 6 n...
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Answered by Mihai V. • Maths tutor
3288 Views

A ball of mass m is thrown from the ground at the speed u=10ms^-1 at an angle of 30 degrees. Find the max height, the total flight time and the max distance it travels?Assume g=10ms^-1 and there is no air friction

First let’s split the problem into 2 parts: Vertical(y direction) and Horizontal(x direction.Vertical: u_y = 10 sin (30) = 5ms^-1 As for the ball to stop at max height and the fall down, all the kinetic ener...
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Answered by Mihai V. • Physics tutor
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