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To differentiate this function you will need the chain rule - differentiating what's inside the brackets and multiplying it by differentiating what's outside the brackets. In this case sin(2x) goes to 2co...

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 ...