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Differentiate x^(4) + x^(1/2) + 3x^(5)

When considering a term in the form of xⁿ, we use the rule nx^n-1 when differentiating.

So, we multiply the power of x by the coefficient (number in front) of x and then minus ...

Answered by Emily P. • Maths tutor

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Solve the simultaneous equations: x^2 + 8x + y^2; x - y = 10.

Label the two equations.

x² + 8x + y² = 84 (1)
x - y = 10 (2)

Rearrange (2) to get y = x - 10 and substitute for y in (1) to get x² + 8x + (x - 10)

Answered by Lewis T. • Maths tutor

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What is the binomial theorem and why is it true?

The binomial theorem is an algebraic formula for the expansion of powers of an expression with two terms (a binomial). For example, we can use it to calculate the polynomial expansion of, say, (1+x)^n for...

Answered by Jacob C. • Maths tutor

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A curve C has the equation x^3 +x^2 -10x +8. Find the points at which C crosses the x axis.

Factorise: (x-2)(x+4)(x-1)

Set equal to 0: (x-2)(x+4)(x-1) = 0

Points are (2,0) (-4,0) (1,0)

Answered by William F. • Maths tutor

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How to plot quadratic functions, e.g. F(x)= x^2 + 2x +1

What we require to plot this graph are the following: the general shape of the graph, the intercepts with the x and y axes and the maximum point/minimum point. All functions with x² as the high...

Answered by Alexandra S. • Maths tutor

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