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

The derivative of sin(cos(x^2)) is -2xcos(cos(x^2))sin(x^2)

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

The first derivative of sin(cos(x^2)) is -2xcos(cos(x^2))sin(x^2)

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derivative of

sin (cos (x^{2}))

- 2 x cos (cos (x^{2})) sin (x^{2})

Solution steps

\frac{d}{d x} (sin (cos (x^{2})))

Apply the chain rule:

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

= cos (cos (x^{2})) \frac{d}{d x} (cos (x^{2}))

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

= cos (cos (x^{2})) (- sin (x^{2}) \cdot 2 x)

Simplify

= - 2 x cos (cos (x^{2})) sin (x^{2})

What is the derivative of sin(cos(x^2)) ?
The derivative of sin(cos(x^2)) is -2xcos(cos(x^2))sin(x^2)
What is the first derivative of sin(cos(x^2)) ?
The first derivative of sin(cos(x^2)) is -2xcos(cos(x^2))sin(x^2)