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let y=sec(x) = 1/(cos(X)) = cos(x)^-1

Thus dy/dx = -1(cos(x))^-2(-sinx) = sin(x)/(cos(x))²

= 1/cos(x)  x  sin(x)/cos(x)

=sec(x)t...

The chain rule is used when we have a function in the form f(g(x)).

For example sin(x^3). [In this case, f(x) = sin(x) and g(x) = x^3]

The chain rule says that the derivativ...

When you differentiate, you multiply by the old power and decrease the power by 1. If the expression has a constant in it, this differentiates to 0. 

So the answer is 3y^(3-1) + ...

This is a simple partial fraction to solve as the denominator has already been given to you as a factorised quadratic. 

Because the x terms are to the dgree 1 aka x¹ we use the...

since f(x)=0 write

9x²-4=0

move the x's to one side and the numbers to the other.

so 9x²=4

then to get rid of the 9 divide ...