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Prove the Quotient Rule using the Product Rule and Chain Rule

given that the chain rule is d/dx(f(g(x))) = g'(x)f'(g(x))given that the product rule is d/dx(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)given that the quotient rule is d/dx(f(x)/g(x)) = (g(x)f'(x) - g'(x)f(x))/(g(x))...
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Derive the formula for differentiation from first principles

For a curve of f(x) against x, we can take the general point (x, f(x)) on the curve. By moving horizontally along the x-axis a distance of h, we also have the point (x+h, f(x+h)) on the curve. The gradient o...
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Answered by Nicola G. • Maths tutor
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Circle the number that is closest in value to (1.1)/(0.0204) [From selection of 5, 6, 50, 60] [Edit of 2018 Paper 1 Q4]

To simplify the question, the denominator can be rounded to 0.02 (to find an estimate), which comes out to be 1.1/0.02=55, which suggests that the answer is between 50 and 60, and not the other two.Now, an a...
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Answered by Doug L. • Maths tutor
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A sphere has a surface area of 4m^2, radius r. Another sphere has radius 2r. Calculate the Volume of the second sphere in M^3.

The surface area of a sphere can be calculated using Area = 4 x Pi x r^2. Since we know the surface are of the first sphere is 4m^2, we can write: 4 = 4 x Pi x r^2. This simplifies to r^2 = 0.318. Taking the...
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Answered by Freddie W. • Maths tutor
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If the base of an equilateral triangle is 3cm, and the height is 5cm, what is the area?

Area of a triangle = 1/2 x base x height 3 x 5 = 15cm1/2 of 15 = 7.5 Area = 7.5cm 2
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