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How do I expand a bracket to a negative power if it doesn't start with a 1.

Okay so consider (2 + x)^-1, we can only do the expansion we know if the bracket starts with a 1, to fix this we can factor a 2 out of the bracket so that it becomes (2(1 + x/2))^-1. Then by our rules of pow...
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Answered by Shaun M. • Maths tutor
4396 Views

Differentiate(dx) xy+4y-13

As this is not in the common form and is HomogeneousStudents should be confident to understand what differentiation does.Using the quotient rule as well as implicit differentiation we look at each part of th...
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Answered by Nojus M. • Maths tutor
3421 Views

Find the turning points of the curve y=2x^3 - 3x^2 - 14.

First differentiate the equation: dy/dx = 6x^2 - 6xSet this equal to 0 as at turning points the change in gradient is 0: 0 = 6x^2 - 6x6x(x-1)=06x=0 therefore x=0(x-1)=0 therefore x=1x=1,0Now substitute back ...
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Answered by Edward R. • Maths tutor
5942 Views

y = arcsec(x), Find dy/dx.

The key to this problem is to apply sec to both sides, and then differentiate implicitly: sec(y)=x; dsec(y)/dx = 1; tan(y)sec(y)dy/dx = 1; dy/dx = 1/(tan(y)sec(y)). Then using the fact that sec(y)=x and tan ...
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Answered by Nicholas Y. • Maths tutor
5305 Views

When solving a trigonometric equation, like sin(x) = -1/3 for 0 ≤ x < 2π, why do I get an answer outside the range? Why are there many correct answers for the value of x?

Drawing the graphs of the trigonometric functions sin, cos &amp; tan, we can see that they all extend along the x-axis to infinity. Indeed, the sin &amp; cos functions move between 1 and -1 on the y-axis, an...
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Answered by Alexandra G. • Maths tutor
9915 Views