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Differentiate x^x and sketch it

Write y = x^xln(y) = xln(x)1/y dy/dx = (1+ln(x)) by applying the chain rule to the LHS and product rule to the RHSdy/dx = y(1+ln(x)) Rearranging dy/dx = x^x (1+ln(x)) Substituting y=x^x into the equationNote...
JN
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If f(x) =x^2 - 5x + 7 what are the coordinates of the minimum of f(x-2)?

The easiest way to do this is to notice that f(x-2) is just f(x) translated by two in the positive x-direction - it is not necessary to calculate what f(x-2) is at any point! So we calculate f'(x) = 2x - 5Se...
JN
Answered by James N. • MAT tutor
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Why does integration by parts work?

Recall the product rule for differentiation: the derivative of uv is equal to u'v+uv'.If we use the fact that integration reverses differentiation (so the integral of f' is f), then we calculate that uv is e...
TB
Answered by Thomas B. • Maths tutor
5254 Views

How influential are pressure groups in the USA

Pressure groups have been very influential in the USA because they are able to shape debate, shape agenda and determine outcomes. However others have argued that party and voters have more influence than pre...
SH
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Asteroid of mass 10^16 kg is travelling in the equatorial plane of Earth. It hits the surface at 45°. After the impact the day shortens by 1% (15 mins). How fast was the asteroid - comment? Neglect effects of atmosphere. Consider only inelastic collision.

Key idea - total angular momentum of the system is conserved. Before the collision: angular momentum of earth is given by L E =I w E , here w E is the angular velocity of Earth and I is its moment of innerti...
JK
Answered by Jiri K. • Physics tutor
2676 Views