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Find dy/dx when x+2y+3y^2= 2x^2+1

To solve this question we can use implicit differentiation. We can write:d/dx(x+2y+3y^2)=d/dx(2x^2+1).When differentiating something in terms of y with respect to x we can use the chain rule, this allows ...

Answered by Adam G. • Maths tutor

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Solve D/dx (ln ( 1/cos(x) + tan (x) )

Solve D/dx (ln ( 1/cos(x) + tan (x) ) As always, we approach with a substitution method that we would normally use for differentiating ln (x). So, we try differentiate ln (t) with t= 1/cos(x) + tan(x)So w...

Answered by Amera D. • Maths tutor

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let line L have the equation 4y -3x =10, and line M passes through the points (5,-1) and (-1,8), find out if they are perpendicular, parallel, or neither

L:4y=3x+10 -> y=3/4 x + 10/3. M: y= mx+ c such that it passes through the points in question, then m=(-1-8)/(5-(-1))=-3/2. As the gradient of L is not a negative reciprocal of the gradient of M, nor is...

Answered by Illya N. • Maths tutor

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Integrate 2x^3 -4x +5

2x³- 4x + 5For integration we add 1 to the power, and divide by the new powerso: (2x³⁺¹ )/4 - (4x¹⁺¹)/2 +5x⁰⁺¹=1/2 x⁴- 2x²+ 5x

Answered by Anne Elizabeth G. • Maths tutor

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The normal to the curve C when x=1 intersects the curve at point P. If C is given by f(x)=2x^2+5x-3, find the coordinates of P

Differentiate C:dy/dx=4x+5When x=1dy/dx=4(1)+5dy/dx=9This is gradient of tangent.Gradient of normal=-1/9When x=1, y=4y-4=-1/9(x-1)y=(-1/9)x+(37/9)(-1/9)x+(37/9)=2x^2+5x-30=2x^2+(46/9)x-(64/9)x=1 or x=-32/...

Answered by Hannah C. • Maths tutor

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