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Find the derivative with respect to x and the x-coordinate of the stationary point of: y=(4x^2+1)^5

y=(4x^2+1)^5 y=u^5 u=4x^2+1 y’=5u^4 (wrt u) u’=8x y’=40x(4x^2+1)^4 y’=40x(4x^2+1)^4=0 x=0 (x^2+1>0)
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Answered by Ellie B. • Maths tutor
4599 Views

Differentiate x^2 + xy + y^2 =1 implicitly.

Each part can be done separately, so x^2 becomes 2x, xy becomes dy/dx + y by product rule, y^2 becomes 2y(dy/dx) by chain rule, and 1 becomes 0. Hence the answer is 2x + y + (2y+1)dy/dx = 0, but the answer i...
TD
Answered by Tutor80806 D. • Maths tutor
6340 Views

6y+2x^2=6 x=(y+1)^0.5 solve the simultaneous equations

x^2=y+1 therefore 6y+2y+2=6 therefore 8y=4 y=0.5 sub in to either equation x=(3/2)^0.5
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Answered by Thomas F. • Maths tutor
3452 Views

Differentiate 3x^2+1/x and find the x coordinate of the stationary point of the curve of y=3x^2+1/x

To differentiate we multiply by the power and take one off the power. d/dx(3x^2+1/x)= 6x-1/x^2 At a stationary point the gradient equals zero 6x-1/x^2=0 which rearranges to x=(1/6)^(1/3)
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Answered by Rachel W. • Maths tutor
5009 Views

Let Sn be the sum of the first n terms of the arithmetic series 2 + 4 + 6 + ... i) Find S4

Firstly look for key terms in the question, identifying that we are going to be finding the sum of n terms, and it is an arithmetic series . This allows us to know which equations to look for in our formula ...
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Answered by Sydney L. • Maths tutor
6558 Views