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Find the equation of the tangent of the curve y = (8x)/(x-8) at the point (0,0)

We will be using the quotient rule, although the product rule is also usable and can be run through if the student wishes. Firstly, define u = 8x, v = x-8 for simplicity. Then clearly u' = 8, v' = 1, and so ...
TK
Answered by Timofey K. • Maths tutor
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Differentiate sin(x^3) with respect to y

For this we must use the chain rule. We start by defining x 3 as a new variable, u = x 3 Can then rewrite the expression as y = sin(u) Chain rule tells us that dy/dx = (dy/du)(du/dx) We can calculate these i...
LB
Answered by Lloyd B. • Maths tutor
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Solve the simultaneous equations; 3x+2y=11 and 2x-2y=14

2y=11-3x and 2y=2x-14 11-3x=2x-14 25=5x thus x=5 3(5) +2y=11 2y=-4 thus y=-2
HS
Answered by Harrie S. • Maths tutor
7673 Views

Expand the following expression: -5x(x-7)(x+3)

Expansion of the given expression will result in x to the 3rd power, as there are 3 parts involving x, multiplied together. Let's ignore -5x for a second, and multiply the two expressions in brackets (using ...
MS
Answered by Matas S. • Maths tutor
5613 Views

The curve has equation y = x^3 - x^2 - 5x + 7 and the straight line has equation y = x + 7. One point of intersection, B, has coordinates (0, 7). Find the other two points of intersection, A and C.

As both equations are equal to y, we can combine them to create a single equation in terms of x: x^3 - x^2 -5X + 7 = x + 7. Shift the equation so the left hand side is equal to 0 on the right: x^3 - x^2 - 6x...
AB
Answered by Alfie B. • Maths tutor
7960 Views