What is the derivative of cos((1-x^2^2)) ?

The derivative of cos((1-x^2^2)) is 4xsin((1-x^2)^2)(1-x^2)

What is the first derivative of cos((1-x^2^2)) ?

The first derivative of cos((1-x^2^2)) is 4xsin((1-x^2)^2)(1-x^2)

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\frac{d}{d x} (cos ((1 - x^{2})^{2}))

4 x sin ((1 - x^{2})^{2}) (1 - x^{2})

Solution steps

\frac{d}{d x} (cos ((1 - x^{2})^{2}))

Apply the chain rule:

- sin ((1 - x^{2})^{2}) \frac{d}{d x} ((1 - x^{2})^{2})

= - sin ((1 - x^{2})^{2}) \frac{d}{d x} ((1 - x^{2})^{2})

\frac{d}{d x} ((1 - x^{2})^{2}) = - 4 x (1 - x^{2})

= - sin ((1 - x^{2})^{2}) (- 4 x (1 - x^{2}))

Simplify

= 4 x sin ((1 - x^{2})^{2}) (1 - x^{2})

What is the derivative of cos((1-x^2^2)) ?
The derivative of cos((1-x^2^2)) is 4xsin((1-x^2)^2)(1-x^2)
What is the first derivative of cos((1-x^2^2)) ?
The first derivative of cos((1-x^2^2)) is 4xsin((1-x^2)^2)(1-x^2)