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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\frac{d}{d x} (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})

\int \frac{2 x ^{2} + 3}{( x ^{2} + 1 ) ^{2}} d x

(x + y) \frac{d y}{d x} = x - y

\int sec^{4} (x) tan^{3} (x) d x

\frac{1 - 2 s}{5 s ^{2} + 8 s + 10}

y^{^{'}} = t + t y^{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)