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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 we, ...
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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 it...
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Answered by Illya N. • Maths tutor
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Integrate 2x^3 -4x +5

2x 3 - 4x + 5For integration we add 1 to the power, and divide by the new powerso: (2x 3+1 )/4 - (4x 1+1 )/2 +5x 0+1 =1/2 x 4 - 2x 2 + 5x
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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=-32/9P ...
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Answered by Hannah C. • Maths tutor
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Differentiate 3x^2 + 4x - 7

In order to differentiate a number, 2 steps are needed to be made. The first is to reduce the power of the number by 1 and then multiply that value to the first number. I will run you through the given quest...
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Answered by James R. • Maths tutor
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