What is derivative of y(θ)=cos(θ^2) ?

The answer to derivative of y(θ)=cos(θ^2) is (dy}{dx}=\frac{-2xsin(x^2)-y)/x

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derivative of y(θ)=cos(θ^2)

derivative of

y = cos (x^{2})

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

Solution steps

y x = cos (x^{2})

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

x \to \infty lim (2 x^{4})

\frac{d y}{d x} = 2 y - x y

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

x \to 1 + lim (\frac{3}{x} - \frac{2}{ln ( x )})

y^{^{'}} + k y = e^{- k x}

What is derivative of y(θ)=cos(θ^2) ?
The answer to derivative of y(θ)=cos(θ^2) is (dy}{dx}=\frac{-2xsin(x^2)-y)/x