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How do we differentiate y = arctan(x)?

Step 1: Rearrange y = arctan(x) as tan(y) = x. Step 2: Use implicit differentiation to differentiate this with respect to x, which gives us: (dy/dx)*(sec(y))^2 = 1. Step 3: Rearrange this equation to give us...
SC
Answered by Solly C. • Maths tutor
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How do you find the integral of sin^2(x) dx?

Sin^2(x) cannot be integrated in its current form so you must use trigonometric identities to change sin^2(x) into something else. Use the formula for cox(2x): cos(2x)=cos(x+x)=cos^2(x)-sin^2(x) Now use that...
CW
Answered by Chloe W. • Maths tutor
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A curve has equation y = 2x^5 + 5x^4 1 . (a) Find: (i) dy/ dx [2 marks] (ii) d^2y/ dx^2 (b) The point on the curve where x ¼ 1 is P. (i) Determine whether y is increasing or decreasing at P, giving a reason for your answer.

a.) dy/dx+10x^4+20x^3 d^2y/dx^2=40x^3+60x^2 b.)sub in x=-1 to dy/dx=10(-1)^4+20(-1)^3 =-10 therefore, decreasing
AF
Answered by Alexandra F. • Maths tutor
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Explain the Chain Rule

The chain rule is used to differentiate composite functions, ie "a function of a function". In this case we have an outer function and an inner function. For example Differentiate f(g(x)). Here f i...
AC
Answered by Alex C. • Maths tutor
4659 Views

What is the angle between the position vectors a and b, where a = (6i - j + 3k) and b = (-4i + 2j + 10k)?

cos( AOB ) = a.b /(| a | x | b |) a.b = (6i - j + 3k) . (-4i + 2j + 10k) = (6 x -4) + (-1 x 2) + (3 x 10) = -24 + -2 + 30 = 4 (| a |)^2 = 6^2 + (-1)^2 + 3^2 = 36 + 1 + 9 = 46 -> | a | = 46^(1/2) (| b |)^2...
DH
Answered by David H. • Maths tutor
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