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Let’s check out your problem:

y=(5x-3)^(3)

y=(5x−3)3 y=(5 x-3)^{3}

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Full solution

Q. y=(5x−3)3 y=(5 x-3)^{3}
  1. Identify Function: Identify the function to differentiate.\newlineFunction: y=(5x−3)3y = (5x - 3)^3
  2. Apply Chain Rule: Apply the chain rule for differentiation: f(g(x)))' = f'(g(x)) \cdot g'(x)\. Here, \$f(u) = u^3 and g(x)=5x−3g(x) = 5x - 3.
  3. Differentiate f(u)f(u): Differentiate f(u)f(u) with respect to uu.\newlinef′(u)=3u2f'(u) = 3u^2\newlineSubstitute u=5x−3u = 5x - 3:\newlinef′(5x−3)=3(5x−3)2f'(5x - 3) = 3(5x - 3)^2
  4. Differentiate g(x)g(x): Differentiate g(x)g(x) with respect to xx.g′(x)=5g'(x) = 5
  5. Multiply Derivatives: Multiply the derivatives. dydx=f′(5x−3)⋅g′(x)=3(5x−3)2⋅5\frac{dy}{dx} = f'(5x - 3) \cdot g'(x) = 3(5x - 3)^2 \cdot 5
  6. Simplify Expression: Simplify the expression. dydx=15(5x−3)2\frac{dy}{dx} = 15(5x - 3)^2

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