6 Find the equation of the tangent line to the graph of $y=\left(x^{2}-1\right)^{5}$ at $\mathrm{P}(0,-1)$.

Step 1 ：Given the function \(y=(x^{2}-1)^{5}\), we want to find the equation of the tangent line at the point P(0,-1).

Step 2 ：First, we need to find the derivative of the function, which gives us the slope of the tangent line. The derivative of \(y=(x^{2}-1)^{5}\) is \(y'=10x(x^{2}-1)^{4}\).

Step 3 ：Evaluating the derivative at the point P(0,-1), we find that the slope of the tangent line is 0.

Step 4 ：Using the point-slope form of a line, \(y - y_{1} = m(x - x_{1})\), where m is the slope and \((x_{1}, y_{1})\) is a point on the line, we can find the equation of the tangent line.

Step 5 ：Substituting m = 0 and \((x_{1}, y_{1}) = (0, -1)\) into the equation, we get \(y + 1 = 0\).

Step 6 ：Solving for y, we find that the equation of the tangent line is \(y = -1\).

Step 7 ：Final Answer: The equation of the tangent line to the graph of \(y=(x^{2}-1)^{5}\) at P(0,-1) is \(\boxed{y = -1}\).