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The curve C has the equation y = 2x^2 -11x + 13. Find the equation of the tangent to C at the point P (2, -1).

The first step is to differentiate the equation of the curve in order to find the gradient of the tangent at the curve. Remember that when differentiating polynomials, we multiply the index of the variable x...
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Answered by James Y. • Maths tutor
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A curve has the equation (x+y)^2 = xy^2. Find the gradient of the curve at the point where x=1

The first step is to find dy/dx. To do this you must first expand the brackets. x 2 + y 2 + 2xy = xy 2 Then differentiate each term with respect to x. dy/dx of (x 2 ) = 2x dy/dx of (y 2 ) = 2y(dy/dx) (Using ...
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Answered by Motunrayo O. • Maths tutor
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How do I solve this inequality: x^2>2x ?

Solve the equation x 2 =2x (solve x 2 -2x=0 by factorisation). Sketch the graphs y=x 2 and y=2x, using standard graph shapes. Look at the sketch to see for which values of x the graph y=x 2 lies above y=2x; ...
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Answered by Jan K. • Maths tutor
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Differentiate with respect to X: x^2 + 2y^2+ 2xy = 2

Assuming the correct tools of differentiation have been taught, we can tackle each term seperately and then rearrange to have dy/dx as the subject. Taking a look at the first term, x^2, differentiating this ...
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Answered by Callum O. • Maths tutor
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y = x*(x-2)^-1/2. Prove dy\dx = (x-4)/2*(x-2)^3/2

Firstly, when approaching a differentiation question you need to work out what method you need to use to solve it. As you can see there are two terms multiplied by one another (the 'x' term and the '(x-2) -1...
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Answered by Graham R. • Maths tutor
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