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Differentiate arctan(x) with respect to x

We can set arctan(x) = y. Remember that arctan(x) is the inverse of tan(x), so we can take the tangent of both sides to give: tan(arctan(x)) = x = tan(y). Tan(x) has the standard derivative of sec^2(x) (whic...
SE
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A uniform ladder of mass 5 kg sits upon a smooth wall and atop a rough floor. The floor and wall are perpendicular. Draw a free body diagram for the ladder (you do not need to calculate any forces).

Diagram should include two orthogonal lines, representing the wall and floor. Connecting them should be a diaganol line (the ladder) At the midpoint of the line should be a vertical downward arrow whose head...
DG
Answered by Dean G. • Maths tutor
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How do you integrate ?

In order to integrate an algebraic term, such as 8x 3 + 4, one must first take the power of the first term and increase this by 1, getting 8x 4 . Secondly , divide the coefficient on x by the new power, in t...
LH
Answered by Louie H. • Maths tutor
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Discuss the largest threats to biodiversity

Habitat change is one of the most prominent threats to biodiversity, driven by the conversion of natural land to agricultural areas. It leads to large declines in species numbers and species diversity within...
RF
Answered by Rebecca F. • Geography tutor
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Explain the chain rule of differentiation

The chain rule can be used to find more complex derivatives.For example, in the case of: y = (5x + 2) 5 To find the derivative in the ordinary fashion, one would need to expand the brackets to:y=3125x 5 +625...
TH
Answered by Toby H. • Maths tutor
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