Using the fundamental theorem of calculus part 1,find dy/dx given y=
To find dy/dx using the fundamental theorem of calculus part 1, we first need to determine the antiderivative of the function y.
The fundamental theorem of calculus states that if F(x) is an antiderivative of a function f(x) on an interval [a, b], then the definite integral of f(x) from a to b is given by F(b) - F(a).
In this case, since we are given y, we can rewrite it as the integral of dy/dx with respect to x. So our equation becomes:
∫(dy/dx) dx = y + C,
where C is the constant of integration.
Now, we can differentiate both sides of the equation with respect to x. The integral and derivative operations cancel each other out, and we're left with:
dy/dx = d/dx (y + C),
which simplifies to:
dy/dx = 0,
since the derivative of a constant is zero.
Therefore, given y, the derivative dy/dx is equal to zero.