Question

Implicit derivative 1

Find y’(x) from F(x,y) =2^(-x -y) *ln(3*x +3*y) -x -y +(x+y)^3 =20 at (x,y)=(1, 1.824). Write y’(1) at this point as a number in decimal notation with at least two digits after the decimal point. No fractions, spaces or other symbols. Hint: the simple solution does not even require taking derivatives.

Answer 1

From the above equation, we can see that F(x,y) = 20.

This means that F(x,y ) is a constant function. The implicit derivative (y'(x)) will thus be 0 since the function itself is a constant function. The derivative of a constant function is always 0. The rule for differentiating constant functions is called the constant rule. It states that the derivative of a constant function is zero.

Hence, y'(x) at (x,y) = (1, 1.824) will thus be 0. No matter what values of (x,y) we put into the function, y'(x) would always be 0.