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Find an expression in terms of powers of cos(x) for cos(5x)

De Moivre's theorem states that e ix = cos(x) + isin(x) or that e i5x = cos(5x)+ isin(5x). If the real components of both sides of this equation is taken we can see that : cos(5x) = Re[e i5x ] where Re means...
AA
Answered by Arnav A. • Maths tutor
7754 Views

Differentiate f(x)=(x+sin(2x))^4

This is an actual question from an EdExcel C3 paper worth 4 marks. Ok so first thing we do is look at the function and try and determine which of our 3 differentiation rules we use. Is it a Product / Quotien...
UB
Answered by Udayan B. • Maths tutor
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The curve C has the equation 4x^2 - y^3 - 4xy + 2y = 0 . The point P with coordinates (-2, 4) lies on C. Find the exact value of dy/dx at the point P.

4x 2 - y 3 - 4xy + 2 y = 0To find dy/dx we need to differentiate all the terms in the equation. As you may notice the x's and y's are mixed together so we will have to use implicit differentiation. Since we ...
EM
Answered by Esther M. • Maths tutor
10945 Views

Differentiate with respect to x: y=2^x

This question demonstrates how the exponential function can be used to simplify equations. In its current form the equation appears complex and the method is not clear. However, if we take the ln of both sid...
HW
Answered by Hugo W. • Maths tutor
4525 Views

A curve is defined for x > 0. The gradient of the curve at the point (x,y) is given by dy/dx = x^(3/2)-2x. Show that this curve has a minimum point and find it.

This is a typical exam style question, taken from an AQA paper. This question is testing your knowledge of stationary points and differentiation. Step 1: Find all stationary points by setting the first deriv...
YC
Answered by Yishuang C. • Maths tutor
5097 Views