What is the derivative of cos(y(dy)/(dx)) ?

The derivative of cos(y(dy)/(dx)) is -sin(y)(dy)/(dx)^2+cos(y)(d^2y)/(dx^2)

What is the first derivative of cos(y(dy)/(dx)) ?

The first derivative of cos(y(dy)/(dx)) is -sin(y)(dy)/(dx)^2+cos(y)(d^2y)/(dx^2)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (y), g = \frac{d y}{d x}

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

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

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

Simplify

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

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

5 x^{- 4}

\int (x + 1) \cdot (x - x + 1) d x

e^{x + y} d x + d y = 0

\frac{\partial}{\partial z} (4 y (z + 1)^{2})

\int (10 x) d x

What is the derivative of cos(y(dy)/(dx)) ?
The derivative of cos(y(dy)/(dx)) is -sin(y)(dy)/(dx)^2+cos(y)(d^2y)/(dx^2)
What is the first derivative of cos(y(dy)/(dx)) ?
The first derivative of cos(y(dy)/(dx)) is -sin(y)(dy)/(dx)^2+cos(y)(d^2y)/(dx^2)