What is the derivative of sqrt(ycos(x)) ?

The derivative of sqrt(ycos(x)) is (cos(x)\frac{dy)/(dx)-sin(x)y}{2sqrt(cos(x)y)}

What is the first derivative of sqrt(ycos(x)) ?

The first derivative of sqrt(ycos(x)) is (cos(x)\frac{dy)/(dx)-sin(x)y}{2sqrt(cos(x)y)}

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 y cos ( x )} \frac{d}{d x} (y cos (x))

= \frac{1}{2 y cos ( x )} \frac{d}{d x} (y cos (x))

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

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

Simplify

\frac{1}{2 y cos ( x )} (cos (x) \frac{d y}{d x} - sin (x) y) : \frac{cos ( x ) \frac{d y}{d x} - sin ( x ) y}{2 cos ( x ) y}

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

What is the derivative of sqrt(ycos(x)) ?
The derivative of sqrt(ycos(x)) is (cos(x)\frac{dy)/(dx)-sin(x)y}{2sqrt(cos(x)y)}
What is the first derivative of sqrt(ycos(x)) ?
The first derivative of sqrt(ycos(x)) is (cos(x)\frac{dy)/(dx)-sin(x)y}{2sqrt(cos(x)y)}