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Find dy/dx for the following equation: f(x) = x^7 + 7x

Differentiation is used to calculate the rate of change. For example, if you have the speed of a car (velocity), and you want to find out the how the speed has changed over time (acceleration), you can diffe...
TS
Answered by Tola S. • 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
AE
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A straight line passes through the point (0, 6) and is perpendicular to y = 4x - 5. Find the equation of this line, giving your answer in the form y = mx + c .

perpendicular so the gradient is -1/4 y= -1/4x +CSub in the coordinate (0,6) 6 = -1/4 (0) +C C=6y=-1/4x +6
MS
Answered by Maria S. • Maths tutor
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factorise x^2 - 8x -65

Two numbers add/ subtract to make -8Two numbers multiply to make -65. These are 1 and 65 as well as 5 and 13Seeing as 1 and 65 cant add or subtract to make -8 the numbers we'll use are 5 and 13. These also s...
KC
Answered by Kavi C. • Maths tutor
5625 Views

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 ...
HC
Answered by Hannah C. • Maths tutor
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