Questions: Find d²y/dx². y=1/x¹¹

Transcript text: Find $\frac{d^{2} y}{d x^{2}}$. \[ y=\frac{1}{x^{11}} \]

Solution

Solution Steps

Step 1: Identify the Function Type

The function is a power function of the form $f(x) = x^{11}$.

Step 2: Calculate the First Derivative

Apply the power rule to find the first derivative, $\frac{dy}{dx} = 11x^{10}$.

Step 3: Calculate the Second Derivative

Apply the power rule again to find the second derivative, $\frac{d^2y}{dx^2} = 11(10)x^{9}$, which simplifies to $\frac{d^2y}{dx^2} = 110$ at $x = 1$.

Final Answer:

The second derivative of the function at $x = 1$ is $\frac{d^2y}{dx^2} = 110$.

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