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How would you differentiate ln(sin(3x))?

To answer this question we require the chain rule, which states that dy/dx=(dy/du)*(du/dx) To use this formula in our question, we can let y=ln(sin(3x))=ln(u) where u=sin(3x) Firstly, using a standard result...
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Answered by Hannah D. • Maths tutor
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Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

First, write the line in vector form r =(1 1 1) + t(1 2 -1). Consider a point P on the line such that the line connecting P and A is perpendicular to L. The vector P->A is (2 3 4) - (1 1 1) - t(1 2 -1) = ...
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Answered by Zac T. • Maths tutor
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Prove that the difference of any two consecutive square numbers is odd

It is important we first define what we mean by an odd and even number. An even number is any integer (whole number) number divisible by 2 so we can express any even number as 2x where x is any integer. When...
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Answered by Amar H. • Maths tutor
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What is the Pythagoras Equation?

a^2 + b^2 = c^2
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Answered by Nancy N. • Maths tutor
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Differentiate y = e^(x^2 - 3x).

This question is an example of the chain rule for differentiating. Firstly, identify the inner function. In this case, it is x 2 - 3x. This function must be differentiated first: d/dx (x 2 - 3x) = 2x - 3 Sec...
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Answered by Ellie S. • Maths tutor
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