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Finding a Derivative of the function. 9. y=(2x-7)^(3)

Finding a Derivative of the function.\newline99. y=(2x−7)3 y=(2 x-7)^{3}

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Q. Finding a Derivative of the function.\newline99. y=(2x−7)3 y=(2 x-7)^{3}
  1. Identify Function: Identify the function to differentiate. The function is y=(2x−7)3y=(2x-7)^{3}.
  2. Find Derivative of Inner Function: Find the derivative of the inner function, u(x)=2x−7u(x) = 2x-7. The derivative of u(x)u(x) is 22.
  3. Apply Chain Rule: Apply the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. So, the derivative of y=(2x−7)3y=(2x-7)^{3} is 3⋅(2x−7)2⋅23\cdot(2x-7)^{2}\cdot2.
  4. Simplify Derivative Expression: Simplify the derivative expression. The derivative of y=(2x−7)3y=(2x-7)^{3} is y′y'(x) = 6⋅(2x−7)26\cdot(2x-7)^{2}.

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