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Find the derivative (dy/dx) a) y = cos(5x^3 + 2x -3) b) y = cos^3(5x^3+2x-3)

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Find the derivative (dy/dx)

a) y = cos(5x^3 + 2x -3)

b) y = cos^3(5x^3+2x-3)

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a) You should use the chain rule to differentiate y with respect to x such that:

`(dy)/(dx) = (cos(5x^3 + 2x -3))'*(5x^3 + 2x -3)'`

`(dy)/(dx) = (-sin (5x^3 + 2x -3))*(15x^2 + 2)`

Hence, differentiating the function y with respect to x yields `(dy)/(dx) = (-sin (5x^3 + 2x -3))*(15x^2 + 2).`

b) You should also use the chain rule to differentiate y with respect to x such that:

`(dy)/(dx) = (cos^3(5x^3 + 2x -3))'*(cos(5x^3 + 2x -3))'*(5x^3 + 2x -3)'`

`(dy)/(dx) = 3(cos^2(5x^3 + 2x -3))*(-sin (5x^3 + 2x -3))*(15x^2 + 2).`

Hence, differentiating the function y with respect to x yields `(dy)/(dx) = 3(cos^2(5x^3 + 2x -3))*(-sin (5x^3 + 2x -3))*(15x^2 + 2).`

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