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If y = 1/(x^2) + 4x, find dy/dx

First, notice that 1/(x^2) = x^(-2)dy/dx = d/dx (x^(-2) + 4x)The derivative of the sum is the sum of the derivatives= d/dx (x^(-2)) + d/dx (4x)The derivative of x^n is nx^(n-1), for every real number n, a...

Answered by Bogdan-Adrian M. • Maths tutor

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Given that (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2) = 7, show that tan(x)^2 = 3/2

First, we use 1 - sin(x)^2 = cos(x)^2 and get:(LHS) (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2)= (cos(x)^2 + 4 sin(x)^2)/cos(x)^2= 1 + 4 (sin(x)/cos(x))^2= 1 + 4 tan(x)^2Now we know that the left hand side is eq...

Answered by Bogdan-Adrian M. • Maths tutor

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The surface run-off of nitrate from agricultural fertiliser into freshwater ponds and lakes can cause the death of the fish. Explain how this happens.

This question crops up a lot and may be up to a five mark question, if you learn the key points and terms you can be confident of getting all the marks you can here!

First of all,

Answered by Sarah M. • Biology tutor

5268 Views

When do I need to put an accent (pronunciation rules)?

Spanish is great because it is a language which is completely phonetic, which means it is read exactly how it is written and always follows certain rules. One of those rules is about stress. All multi-...

Answered by Sebastian B. • Spanish tutor

4400 Views

What does a negative velocity mean?

To understand this question, it is important to know that velocity has both a direction and a magnitude. The magnitude can be expressed by the unit m/s, however the direction is expressed by a vector. ...

Answered by Thomas D. • Physics tutor

33982 Views