Find the derivative of $ cos(x^2) $ with respect to $ x $

To find the derivative of $ \cos(x^2) $ with respect to $ x $, we use the chain rule:

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$ \frac{d}{dx} \cos(u) = -\sin(u) \cdot \frac{du}{dx} $

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Here, let $ u = x^2 $. Then:

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$ \frac{du}{dx} = \frac{d}{dx}(x^2) = 2x $

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Now apply the chain rule:

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$ \frac{d}{dx} \cos(x^2) = -\sin(x^2) \cdot 2x $

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The final derivative is:

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$ \frac{d}{dx} \cos(x^2) = -2x \sin(x^2) $

To find the derivative of $ cos(x^2) $, use the chain rule:

$ frac{d}{dx} cos(u) = -sin(u) cdot frac{du}{dx} $

Let $ u = x^2 $, so:

$ frac{d}{dx} cos(x^2) = -sin(x^2) cdot 2x $

To find the derivative of $ cos(x^2) $, use the chain rule:

$ frac{d}{dx} cos(u) = -sin(u) cdot frac{du}{dx} $

Let $ u = x^2 $, so:

$ frac{d}{dx} cos(x^2) = -sin(x^2) cdot 2x $

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