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Calculate the derivative of the following function: f(x)=cos(3x))^2

The answer can be found by using the chain rule and simple substitution as well as basic knowledge of differentiation.f’(x)= -6cos(3x)sin(3x)

JM
Answered by Jeff M. Maths tutor
4764 Views

What are the most important trig identities we need to know?

cos^2(A) + sin^2(A) = 1, sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB, sin2A = 2sinAcosA (if A = B), cos2A = cos^2(A) - sin^2(A) (if A = B), cos2A = 1 - 2sin^2(A) => sin^2(A) = 1/2(1 ...

BH
Answered by Bowen H. Maths tutor
4272 Views

Solve the differential equation dy/dx = 6xy^2 given that y=1 when x=2.

This equation can be solved using separation of variables. Firstly we rearrange the equation so that all of the y's are on the left hand side and all of the x's are on the right: 1/y2* dy = 6x ...

WS
Answered by Will S. Maths tutor
7125 Views

Find the binomial expansion of (4-8x)^(-3/2) in ascending powers of x, up to and including the term in x^3. Give each coefficient as a fraction in its simplest form. For what range of x is a binomial expansion valid?

(4-8x)^(-3/2) =Factoring out 4^(-3/2) to make binomial expansion easier(1-2x)^(-3/2) =Using the binomial series expansion in the formula booklet, up to the term in x^3<...

HT
Answered by Hamish T. Maths tutor
8608 Views

'In memory, war seems like a dream' (Samual Hynes, The Soldiers Tale, 1997) Compare the significance of remembering in two other texts you have studied. Remember to include in your answers reference to how meanings are shaped in the texts you are comparin

‘In memory war seems like a dream’ for an audience in the modern day the reality of war, although we possess more knowledge, it is impossible for us to imagine. Remembrance can be disturbing but also comf...

SI
3914 Views

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