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Differentiate, from first principles, y=x^2

According to first principles, the differential is found as the limit as h->0 of:[f(x+h)-f(x)] / hif we set our f to x^2, then we find that this expression becomes (x^2+2hx+h^2 - x^2)/hWhich simplifies to...
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Answered by Milo E. • Maths tutor
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How do i know where a stationary point is and what type of stationary point it is?

Stationary points are points on a curve where the gradient is zero. There are three types of stationary point maximum, minimum and point of inflexion. (will draw diagrams). They can be found by differentiati...
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Answered by Omar H. • Maths tutor
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Given that w=x * e^-w use implicit differentiation to show that dw/dx=1/(e^w + x)

Given that w=x e -w use implicit differentiation to show that dw/dx = 1/(e w +x)Answer:Use product rule to simplify:dw/dx = x (de -w /dx) + e -w (dx/dx)Use chain rule to simplify even further:dw/dx = -x e -w...
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Answered by Panagiota G. • Maths tutor
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The perimeter of a right angled triangle is 72cm. The length of its sides are in the ratio 3:4:5. Work out the area of the triangle.

Total perimeter - 72cm. Perimeter - (3+4+5)x -> 72=12x therefore x=6. The area of the triangle is 0.5(3x 4x) (because 5x is the longest side) therefore the answer is 0.5(18 24) = 216cm^2
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Answered by Sam T. • Maths tutor
3476 Views

Without expanding any brackets work out the exact solutions of 9(x+3)^2=4

Divide through by 9 giving:(x+3) 2 = 4/9 Square root both sides remembering a square root is plus or minus the answer x+3 = +/-sqrt(4/9) sqrt(4/9)=2/3for the first solution x+3 = 2/3 or x = -7/3for the secon...
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Answered by Thomas B. • Maths tutor
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