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What are logarithms?

Logarithms allow us to calculate and manipulate indices in relation to regular numbers. The key thing to remember is that " log x y " begs the question "which power of x gives y ". By thi...
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Answered by Alex M. • Maths tutor
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Find the derivative of the equation y = x*ln(x)

y = x*ln(x)Let u = x, v = ln(x) => du/dx = 1, dv/dx = 1/x=> y = uv=> dy/dx = (du/dx)v + u(dv/dx) USING PRODUCT RULETherefore y = ln(x) + 1
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Answered by Owen B. • Maths tutor
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Differentiate z = e^(3y^2+5) with respect to y. (Hint: use chain rule.)

We can find dz/dy using chain rule dz/dy=dz/du x du/dy (1) by defining u=3y^2+5 (since the exponent of e is a function of y we call this function u) and rewrite z=e^u. Then, we find dz/du=e^u (2) and du/dy=6...
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Answered by Sophie H. • Maths tutor
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Given y = 4x/(x^2 +5) find dy/dx, writing your answer as a single fraction in its simplest form

This function is fraction so the easiest method is to use the quotient rule (though the product rule can be used). Recall the quotient rule dy/dx = [vu' - uv']/[v^2]Note, u and v refer to the numerator and d...
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Answered by Laurence C. • Maths tutor
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A particle is placed on a rough plane which is inclined to the horizontal at an angle θ, where tanθ =4/3, and released from rest. The coefficient of friction between the particle and the plane is 1/3. Find the particle's acceleration.

Start by drawing a diagram with all of the information from the question on it, as well as the forces acting on the particle. As forces can be divided into their component parts, we can look at the question ...
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Answered by Tutor121490 D. • Maths tutor
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