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How to differentiate using the chain rule

The chain rule is a rule of differentiation that states: (f(g(x))'=f ' (g(x))g'(x) In effect, the chain rule allows us to split up a complicated equation into smaller more manageable chunks. Rather than diff...
AT
Answered by Anthony T. • Maths tutor
4158 Views

Find, w.r.t to x, both the derivative and integral of y=6*sqrt(x)

Understand the question: 'w.r.t' stand for 'with respect to', so the qestions is asking for the dericative and integral to be calcuated in terms of x - so find dy/dx and (integral sign) y dx. Sqrt(x) is the ...
JR
Answered by Jake R. • Maths tutor
5293 Views

Solve the differential equation: (dy/dx) = 6xy^2

Start by recognising that this is a separable differential equation; it can be written with all of the x's on one side of the equals sign, and all of the y's on the other. The first step is to rearrange so t...
MJ
Answered by Michael J. • Maths tutor
10730 Views

intergrate xcos(2x) with respect to x

The function of x has two separate x terms multiplied by each other. Therefore, the appropriate way to integrate this function is by parts. The equation for integration by parts is [integral (u.dv/dx)] = uv ...
MI
Answered by Mark I. • Maths tutor
6782 Views

Having a rectangular parking lot with an area of 5,000 square yards that is to be fenced off on the three sides not adjacent to the highway, what is the least amount of fencing that will be needed to complete the job?

We can turn this into a constrained optimization problem. Let's denote x the side of the parking lot that is perpendicular to the highway, and y the side that is parallel to the highway. We therefore need to...
EB
Answered by Emil B. • Maths tutor
6653 Views