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When differentiating the product of two functions, we need to use the product rule. The theory of it is: (fg(x))'=f'(x)g(x) + f(x)g'(x). This explanation is-differentiate the first function and leave the ...

fist of all you rearrange the equation so you have the x in one side so the equation would look like this: 5x+4x = 1, then you add up the x´s and divide both sides by 9 so the solution would be x= 1/9

For a quadratic equation ax^2 +bx +c = 0 with equal roots we know the discriminant b^2-4ac must equal 0. From our equation we have a=1, b=4k and c=2(k+1) so using b^2-4ac = 0 we have (4k)^2 -412(...

Here, we must first rearrange our equation so all x terms are on one side and all y terms are on the other. Multiplying both sides by dx and diving both by y^(1/2) gives us y^(-1/2)dy = sin(x/2)dx, which ...

To answer, we must be familiar with several trigonometric identities and expressions; first notice that tan(x)=sin(x)/cos(x). Now our function is a quotient of two functions of x that we can easily differ...