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For the following equation, evaluate (dy)/(dx) when x=2. y=x^(4)+5x Answer:

For the following equation, evaluate dydx \frac{d y}{d x} when x=2 x=2 .\newliney=x4+5x y=x^{4}+5 x \newlineAnswer:

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Q. For the following equation, evaluate dydx \frac{d y}{d x} when x=2 x=2 .\newliney=x4+5x y=x^{4}+5 x \newlineAnswer:
  1. Identify Problem Type: Identify the type of problem and the method to solve it. We need to find the derivative of the function yy with respect to xx, and then evaluate it at x=2x=2. This is a differentiation problem.
  2. Differentiate Function: Differentiate the function y=x4+5xy=x^{4}+5x with respect to xx. The derivative of x4x^{4} with respect to xx is 4x34x^{3}, and the derivative of 5x5x with respect to xx is 55.
  3. Combine Derivatives: Combine the derivatives to get the expression for dydx\frac{dy}{dx}. The combined derivative is dydx=4x3+5\frac{dy}{dx} = 4x^{3} + 5.
  4. Evaluate at x=2x=2: Evaluate the derivative at x=2x=2. Substitute x=2x=2 into the derivative to get dydx=4(2)3+5\frac{dy}{dx} = 4(2)^{3} + 5.
  5. Calculate Value: Calculate the value of (dydx)(\frac{dy}{dx}) when x=2x=2. The calculation is (dydx)=4(8)+5=32+5=37(\frac{dy}{dx}) = 4(8) + 5 = 32 + 5 = 37.

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