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Differentiate the expression x^6+5x^4+3 with respect to x

Using the general rule d/dx(a*x^n) = a *n * x^(n-1) and the linearity of the derivative operator, we obtain: 6x^5+20x^3+0 = 6x^5+20x^3
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State the interval for which sin x is a decreasing function for 0⁰ ≤ x ≤ 360⁰.

Draw a diagram of the graph y=sin x between the stated interval. Identify the two extrema. Required interval is in between the two points.
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Curves C1 and C2 have equations y= ln(4x-7)+18 and y= a(x^2 +b)^1/2 respectively, where a and b are positive constants. The point P lies on both curves and has x-coordinate 2. It is given that the gradient of C1 at P is equal to the gradient of C2 at P.

y= ln(4x-7)+18 y= a(x^2 +b)^1/2 At x=2 dy/dx = dy/dx and y =y At x =2 y = ln(8-7) +18 y = ln 1 +18 y =18 At x = 2 18=a(4 +b)^1/2 18/(4+b)^1/2= a y=ln(4x-7)+18dy/dx= 4/(4x-7) At x= 2 dy/dx= 4/8-7= 4 y=a(x^2 +...
JM
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Calculate the value of the definite integral (x^3 + 3x + 2) with limits x=2 and x=1

a) Integrate the given expression using integration laws we have learnt to give [(x^4)/4 + (3(x^2))/2 + 2x ] and you do not need a +c constant as we have limits.b) Substitute the limits into the equation we ...
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Solve the inequality 6x - 7 + x^2 > 0

Firstly rearrange the quadratic such that the coefficient of x 2 is positive (already done in this example) and the quadratic is in the form of ax 2 +bx + c, then solve for x, like you would solve a regular ...
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