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Differentiate y=3xe^{3x^2}+2x

We differentiate y with respect to x:Firstly, we apply the Chain rule in the fist part of the RHS. Remembering the chain rule is uv -> u'v+uv', so d(3xe^{3x^2})/dx=3e^{3x^2}+18x^{2}e^{3x^2}now, we simply ...
JA
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Why did Chamberlain embark on the Tariff Reform campaign?

Joseph Chamberlain embarked upon the Tariff Reform campaign in the aftermath of the Boer war to rectify two fundamental problems that were plaguing British society and industry. Chamberlain outlines his reas...
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Answered by Bethan K. • History tutor
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A particle of mass 0.5 kg is moving down a rough slope (with coefficient of friction = 0.2) inclined at 30 degrees to the horizontal. Find the acceleration of the particle. Use g = 9.8 ms^-2.

Resolving perpendicular to the plane : R - mg cos30 = 0 . Therefore, R = m g cos30 , where R is the reaction force perpendicular to the plane. Resolving down the plane : ma = m g sin30 - 0.2 R = m g sin30 - ...
MB
Answered by Matthew B. • Maths tutor
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Evaluate f'(1) for the function f(x) = (x^2 + 2)^5

First, we must differentiate the function. To do this we must let the contents of the bracket be equal to 'u'. We now can produce two equations, one by subbing in 'u' into the function f(x) to give us u^5. T...
TU
Answered by Tahrim U. • Maths tutor
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Describe how vaccination can lead to protection against bacterial meningitis (6 marks)

Vaccines provide a dead/inactive form of bacterial meningitis. Phagocytes such as macrophages recognise the antigens of bacterial meningitis as foreign so engulf the pathogen forming a phagosome. The lysosom...
JH
Answered by James H. • Biology tutor
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