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Differentiate the equation y = (2x+5)^2 using the chain rule to determine the x coordinate of a stationary point on the curve.

Use the chain rule as this is a composite function. Let u=2x+5.So the original equation becomes y=(u)^2.Using the chain rule: dy/dx = dy/du * du/dxdy/du = 2udu/dx = 2So dy/dx= 4uSince u=2x+5, dy/dx = 4(2x+5)...
DP
Answered by Daniel P. • Maths tutor
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Show that 2sin(x) =(4cos(x)-1)/tan(x) can be written as: 6cos^2(x)-cos(x)-2=0

Rearranging gives:4cos(x)-1 = 2sin(x) tan(x) Substituting in tan(x)=sin(x)/cos(x) gives:4cos(x)-1 = 2sin(x) (sin(x)/cos(x))2sin 2 (x)=4cos 2 (x)-4cos(x)Substituting in 2sin 2 (x) = 2-2cos 2 (x) (from the tri...
OT
Answered by Olivia T. • Maths tutor
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The General Form of the equation of a circle is x^2 + y^2 + 2gx +2fy + c = 0. Find the centre of the circle and the radius of the circle in terms of g f and c.

Given a circle in the general form you can complete the square to change it into the standard form.x 2 + 2gx + y 2 +2fy +c = 0 (1). General form of an equation which has the completing the square method appl...
RS
Answered by Rushabh S. • Maths tutor
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a) Integrate ln(x) + 1/x - x to find the equation for Curve A b) find the x coordinate on Curve A when y = 0.

a) Integrate ln(x) by parts: u = ln(x), dv/dx = 1, du/dx = 1/x, v = x int(u dv/dx) = u v - int(du/dx * v) = ln(x)/x - x so int(ln(x) + 1/x - x) = ln(x)/x - x + ln(x) + x^2 + Cb) y = ln(x)/x - x + ln(x) + x^2...
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Answered by Ellie N. • Maths tutor
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Use integration by parts to evaluate: ∫xsin(x) dx.

Since our function is a product of two "mini-functions" of x, we are able to use integration by parts.The trick for this is to correctly set 'u' and 'dv'. 'u' should be labelled as the function whi...
BA
Answered by Bailey A. • Maths tutor
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