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Simple binomial: (1+0.5x)^4

Expand (1+0.5x)4 , simplifying the coefficients. Step 1. Draw Pascal's triangle to find the coefficients 1 ; 1 2 1 ; 1 3 3 1 ; 1 4 6 4 1. As you can see, each row starts and ends with 1. The numbers in betwe...
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Answered by Srikka S. • Maths tutor
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Solve Inx + In3 = In6

To solve Inx + In3 = In6 we must follow some basic log rules, log b ( mn ) = log b ( m ) + log b ( n )if we compare this with the left side of our equation, Inx + In3, we will set m = x and n = 3, mn is ther...
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Answered by Ellie B. • Maths tutor
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Find the values of x, where 0 < x < 360, such that x solves the equation: 8(tan[x])^2 – 5(sec[x])^2 = 7 + 4sec[x]

This question tests a variety of mathematical techniques and knowledge which is integral to A-level mathematics. Note that the highest power of a variable function in the mentioned equation, is 2. It is ther...
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Answered by Osian S. • Maths tutor
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Prove that the derivative of tan(x) is sec^2(x).

Let y = tan(x) Recall the definition of tan(x) as sin(x)/cos(x) Therefore y = sin(x)/cos(x) Use the quotient rule, which states that for y = f(x)/g(x), dy/dx = (f'(x)g(x) - f(x)g'(x))/g 2 (x) with f(x) = sin...
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Answered by Miriam G. • Maths tutor
124691 Views

How do you differentiate a^x?

The quick answer is that d/dx a^x = ln(a) * a^x. But why? Well, let's go through the steps so we can understand why the formula works. Firstly, a^x can be written as (e^(ln(a)))^x because e^(ln(z)) = z as th...
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Answered by Kian M. • Maths tutor
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