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A curve has equation y = 4x + 1/(x^2) find dy/dx.

As in every case dy/dx can be found by differentiating each term individually with respect to x. Let's first tackle the 4x term. As always the derivative can be found by multiplying the term by the power of ...
CH
Answered by Callum H. • Maths tutor
10755 Views

Solve x^2 + 8x +3 = 0 by completing the square.

Using the completing the square method: 1. Notice (x+4) 2 = x 2 + 8x +16 which differs from the question by a constant 2. So we can write: x 2 + 8x + 3 = (x+4) 2 - 13 (check this yourself if you don't see it...
TD
Answered by Tutor21349 D. • Maths tutor
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Integrate 4x^3 + 6x^2 +4x + 3

Each term is integrated according to the formula: ax b --> (a/(b+1))x (b+1) A constant k integrates to kx Since this is indefinite integration, an additional term of +c must be added to the expression. Th...
EH
Answered by Emma H. • Maths tutor
5853 Views

Differentiate y = 2x^3 + 6x^2 + 4x + 3 with respect to x.

Each term is differentiated according to the formula: y = ax b --> dy/dx = b*ax (b-1) Constants differentiate to zero. Therefore in this example: dy/dx = 6x 2 + 12x + 4
EH
Answered by Emma H. • Maths tutor
7917 Views

Find the gradient of a curve whose parametric equations are x=t^2/2+1 and y=t/4-1 when t=2

Remember that the gradient of a curve is expressed as dy/dx. This can be solved by using the chain rule: dy/dx = dy/dt*dt/dx. The dt in the denominator of the first term, and the numerator of the second term...
AS
Answered by Abigail S. • Maths tutor
9551 Views