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A curve C has the equation x^3 + 2xy- x - y^3 -20 = 0. Find dy/dx in terms of x and y.

Every term needs to be differentiated in terms of x: For the x 3 term , differentiated it becomes 3x 2 (multiply the whole term by the initial power, 3, and the reduce the power by 1 and replace it, 3 theref...
ST
Answered by Seb T. • Maths tutor
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Why is the derivative of a function its gradient?

So, the easiest way to start thinking about this is by looking at straight lines. The gradient of a straight line is just its slope, which is the difference in the y values between any two points, divided by...
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Answered by Connor G. • Maths tutor
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integrate x^2 + 3x + 4

For the x 2 term we add one to the power, and then divide by 3 to get x 3 /3 For the next term we add one to the power and divide by the new power to get 3x 2 /2 We do the same for the 4, which just goes to ...
HB
Answered by Harry B. • Maths tutor
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Given that the curve y = 3x^2 + 6x^1/3 + (2x^3)/3x^1, find an expression for the gradient of the curve.

To find the gradient of a curve, you simply differentiate the equation of the curve. The first thing I like to do in any differentiation question is to simplify each expression where you can i.e. whenever th...
TS
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Let y(x) be a function with derivative y'(x)=x^2-2 and y(0) =7. What is the value of y at x = 3?

Integrate to get y(x) = (1/3)x^3 -2x+c where c is a constant. Substitute in our data 7 =y(0) = (1/3)(0)^3 -2*(0) +c = c. So y(x) =(1/3)x^3 -2x+7 and therefore y(3) = (1/3)(3)^3 -2*3 +7 = 9-6+7 = 10
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Answered by Dawn B. • Maths tutor
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