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

For the following equation, find dydx \frac{d y}{d x} .\newliney=x4+x2 y=x^{4}+x^{2} \newlineAnswer: dydx= \frac{d y}{d x}=

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Q. For the following equation, find dydx \frac{d y}{d x} .\newliney=x4+x2 y=x^{4}+x^{2} \newlineAnswer: dydx= \frac{d y}{d x}=
  1. Identify Function: Identify the function that needs to be differentiated. The function given is y=x4+x2y = x^4 + x^2. We will use the power rule for differentiation, which states that the derivative of xnx^n with respect to xx is n⋅x(n−1)n\cdot x^{(n-1)}.
  2. Apply Power Rule x4x^4: Apply the power rule to the first term x4x^4. The derivative of x4x^4 with respect to xx is 4⋅x4−14\cdot x^{4-1} or 4⋅x34\cdot x^3.
  3. Apply Power Rule x2x^2: Apply the power rule to the second term x2x^2. The derivative of x2x^2 with respect to xx is 2⋅x2−12\cdot x^{2-1} or 2⋅x2\cdot x.
  4. Combine Derivatives: Combine the derivatives of both terms to get the derivative of the entire function. The derivative of y=x4+x2y = x^4 + x^2 with respect to xx is dydx=4x3+2x\frac{dy}{dx} = 4x^3 + 2x.

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