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How do you differentiate (2x+xe^6x)/(9x-(2x^2)-ln(x)) w.r.t. x?

This problem requires using the quotient rule, product rule and the chain rule. The derivative of the entire thing is ((du/dx)v-(dv/dx)u)/v^2 where u=2x+xe^6x and v=9x-2x^2-lnx. dv/dx is relatively straitfor...
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Answered by Seth H. • Maths tutor
3698 Views

The equation of a curve is x(y^2)=x^2 +1 . Using the differential, find the coordinates of the stationary point of the curve.

Firstly we need to use product rule to find the dy/dx of the left hand side (LHS). Using implicit differentiation, we know the differential of y^2 is 2y(dy/dx). Then use to product rule to obtain the dy/dy o...
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Answered by Grace C. • Maths tutor
6753 Views

Where do the kinematics equations (SUVAT) come from?

mathematical derivation
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Answered by Kunal P. • Maths tutor
5000 Views

How do I differentiate a quadratic to the power n?

To do this we will use the chain rule, whereby dy/dx = dy/du * du/dx. So if y = (ax^2+bx+c)^n then we will say that u = ax^2+bx+c. Therefore y =u^n. So to find dy/dx we differentiate u with respect to x, whi...
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Answered by Alex A. • Maths tutor
5860 Views

Given that f(x) = (x^2 + 3)(5 - x), find f'(x).

First we must multiply out the brackets, using FOIL (first, outer, inner, last). This gives f(x) = -x^3 + 5x^2 - 3x + 15. Alternatively you could leave the brackets as they are, and use the product rule to d...
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Answered by Chris D. • Maths tutor
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