How do you differentiate this equation implicitly with respect to x: xy + 21 = 0?
I made this example up. There's a problem in my book just like it.
Please explain why you do what you do, thanks.
I made this example up. There's a problem in my book just like it.
Please explain why you do what you do, thanks.
BrainyMe
Favorite Answer
Since you're differentiating implicitly with respect to x, this calls for you to use he chain rule on the term 'xy'. Obviously the derivatives of 21 and 0 will be 0.
First take the derivative with respect to x and that leaves you with y.
Secondly, since we are differentiating with respect to x still take the derivative of y as usual but you will multiply the derivative by this term- dy/dx. So the derivative of the y in the equation would be x*(dy/dx)
You add up both derivatives as you know how to do with the chain rule, and you have the expression below:
y +x(dy/dx) = 0
You solve for dy/dx from there
Anonymous
differentiate the two sides: d/dx [xy - x - 5y - 19] = d/dx [0] d/dx [xy] - d/dx [x] - 5 d/dx [y] - d/dx [19] = 0 x d/dx [y] + y d/dx [x] - a million - 5(dy/dx) - 0 = 0 -- product rule x(dy/dx) + y(a million) - 5(dy/dx) = a million (dy/dx)(x - 5) = a million-y dy/dx = (a million-y) / (x-5)
Ed I
xy = -21
x dy/dx + y = 0
x dy/dx = -y
dy/dx = -y/x