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Differentiate y=(x-1)^4 with respect to x.

Using the chain rule, differentiate the "outside function" and the "inside function", and multiply the two results to get:dy/dx = 4(x-1)^3 * 1 = 4(x-1)^3
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Answered by Samuel H. • Maths tutor
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Find dy/dx in terms of t for the curve given by the parametric equations x = tan(t) , y = sec(t) for -pi/2<t<pi/2.

We know that dy/dx = (dy/dt) * (dt/dx). Differentiating each of the equations with respect to t gives. dy/dt = sec(t) tan(t) and dx/dt = sec 2 (t). Since dt/dx = 1 / (dx/dt) we have that dt/dx = 1/(sec 2 (t)...
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Answered by Oliver C. • Maths tutor
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7x+5y-3z =16, 3x-5y+2z=-8, 5x+3y-7z=0. Solve for x,y and z.

There are three methods to solve these types of silmultaneous equation questions, substitutution, elimination and matrices. In this example we use substitution and elimination.Elimination example.Eq1). 7x+5y...
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Answered by Holly May B. • Maths tutor
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The line PQ is the diameter of a circle, where points P and Q have the coordinates (4,7) and (-8,3) respectively. Find the equation of the circle.

Start by using the formula d = sqrt((x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 )Therefore, substituting in our coordinates from P and Q:Length PQ = sqrt((-8-4) 2 +(3-7) 2 )= sqrt((-12) 2 +(-4) 2 )= sqrt(160)= sqrt(16) x s...
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Answered by Matt C. • Maths tutor
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Prove that 2cot2x+tanx=cotx

2cot2x= 2(1/tan2x)= 2(1/(2tanx/1-tan 2 x))=2(1-tan 2 x)/2tanx= (1-tan 2 x)/tanx(1-tan 2 x)/tanx +tanx=(1-tan 2 x)/tanx +tan 2 x/tanx=1/tanx=cotx
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Answered by Alisa D. • Maths tutor
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