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Maths
A Level

Differentiate ln(x)/x

To differentiate this, we use the quotient rule as we have 2 functions of x as a fraction.

The quotient rule states that:
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CE
9143 Views

Let R denote the region bounded by the curve y=x^3 and the lines x=0 and x=4. Find the volume generated when R is rotated 360 degrees about the x axis.

The area of a circle is given by (pi)r2 and the area generated by R can be considered as an infinite number of circular areas.

Thus, we can write the area gene...

SB
Answered by Stephen B. Maths tutor
5093 Views

Does the equation: x^2+5x-6 have two real roots? If so what are they?

Having two real roots is equivalent to having two intersections with the x axis.

The equation is a parabola (a U shape) so, having two real roots is equivalent to having the lowest point ...

SB
Answered by Stephen B. Maths tutor
4974 Views

Differentiate a^x

  1. Set y=a^x2. Take the natural log of both sides: ln(y)=ln(a^x)3. Using the log rules, simplify: ln(y)=xln(a)4. Differentiate both sides with respect to x: 1/y dy/dx=lna+05. Rearrange: dy/dx=yln(a)6. ...
HK
Answered by Hafsah K. Maths tutor
16734 Views

Find the tangent to the curve y=x^3+3 at the point x=1.

1. Differentiate the Equation of the curve to find the gradient: y'=3x^2

2. The gradient of the tangent is found by substituting x=1 into y'=3x^2: Gradient of tangent=3

3. N...

SK
Answered by Sevenia K. Maths tutor
4334 Views

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