If y = (x^3 – cos x)^5, then y’ =
To find the derivative of y = (x^3 – cos x)^5, we can use the chain rule
To find the derivative of y = (x^3 – cos x)^5, we can use the chain rule. The chain rule states that if we have a function of the form f(g(x))^n, then the derivative of that function is given by n * (f(g(x)))^(n-1) * f'(g(x)) * g'(x).
Applying the chain rule to the given function, we have:
y’ = 5 * ((x^3 – cos x)^5)^(5-1) * (x^3 – cos x)^(5-1) * (3x^2 + sin x)
Simplifying this expression, we get:
y’ = 5 * (x^3 – cos x)^4 * (3x^2 + sin x)
Therefore, the derivative of y = (x^3 – cos x)^5 is y’ = 5 * (x^3 – cos x)^4 * (3x^2 + sin x).
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