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Let g (x) = 2x sin x . (a) Find g′(x) . (b) Find the gradient of the graph of g at x = π .

a) f'(x)=uv'+vu' if f(x)= uv u=2x u'=2 v=sin(x) v'=cos(x) g'(x)=2x cos(x) +2sin(x) b) g'(π) = 2π cos(π)+2sin(π) = 2 π (-1) + 2 (0) g'(π) = -2π
MB
Answered by Matias B. • Maths tutor
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Differentiate sin(x)cos(x) using the product rule.

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))' = cos 2 (x) - sin 2...
MP
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For the equation y=2x+7, what is the gradient and the y intercept?

For all straight line equations as the one above, the equation is y=mx+c where: m is the gradient, c is the y-intercept. Thus from the arrangement of the given equation, gradient = 2 and y-intercept = 7 .
MP
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Explain the what is meant by the 'Separation of Powers' and how the idea pertains to the British Political System

The separation of powers is a concept first articulated by Montesquieu in his book 'The Spirit of the Laws'. In the book Montesquieu puts forward the idea that if the executive, legislative and judicial func...
BT
Answered by Ben T. • Politics tutor
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Explain the differences between Prokaryotes and Eukaryotes.

Essentially the main difference between prokaryotes and eukaryote is that eukaryotes have compartmentalised organelles. This leads to major differences in their structure. Eukaryotes have a nucleus, with mul...
RG
Answered by Rishi G. • Biology tutor
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