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Prove that the d(tan(x))/dx is equal to sec^2(x).

You can express tan(x) as sin(x)/cos(x). Therefore, tan(x)= sin(x)/ cos(x)The quotient rule can be applied here as there is a function of x in the numerator and denominator.Quotient Rule: (v*(du/dx) - u*(dv/...
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Answered by Chinazam U. • Maths tutor
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What is the general rule for differentiation?

In differentiation you multiply the coefficient of the subject (what the value is multiplied by e.g. 3 is the coefficient of 3x 6 ) by its exponent (the power that the value is raised to e.g. the exponent of...
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Answered by Oisin B. • Maths tutor
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How would you differentiate f(x)=3x(2x-1)^2

This question is really straight forward By using the Chain rule: f'(x) = uv' + u'v. let u=3x, so u'=3 let v=(2x-1)^2, so v'=2x2(2x-1)=8x-4 Now, we put this expression altogether: As f'(x) = uv' + u'v f'(x)=...
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Answered by Ruihang Z. • Maths tutor
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Integrate 1/(5-2x) for 3≤x≤4

You must be careful with these sorts of questions as although 1/(5-2x) is equivalent to (5-2x)^-1, when you integrate you would add one to the power and divide by the new power. But if you were to add one to...
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Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1

First we state the formula for sin(x+y) sin(x+y) = sin(x)cos(y) + cos(x)sin(y) Letting y = 2x sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x) Now sin(2x) = 2sin(x)cos(x) and cos(2x) = 1 - 2sin^2(x), substitute the...
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Answered by Kyle R. • Maths tutor
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