Find the instantaneous rate of change of y = 11x⁵ with respect to x at a general point x₀. A) 55x₀⁵ B) 11x₀ C) 11x₀⁵ D) 11x₀⁴ E) 55x₀⁴

Question

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The instantaneous rate of change of a function $y = 11x^{15}$ with respect to $x$ is found by taking the derivative of the function with respect to $x$. The derivative, using the power rule, is $dy/dx = 11 \cdot 15x^{15-1} = 165x^{14}$, which simplifies to $55x^{14}$ after factoring out a common factor of 3.

Find the Instantaneous Rate of Change of Y = 11x5

Find the Instantaneous Rate of Change of Y = 11x⁵