What is the derivative of y*cos(x) ?

The derivative of y*cos(x) is cos(x)(dy)/(dx)-sin(x)y

What is the first derivative of y*cos(x) ?

The first derivative of y*cos(x) is cos(x)(dy)/(dx)-sin(x)y

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = cos (x)

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

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

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

Simplify

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

What is the derivative of y*cos(x) ?
The derivative of y*cos(x) is cos(x)(dy)/(dx)-sin(x)y
What is the first derivative of y*cos(x) ?
The first derivative of y*cos(x) is cos(x)(dy)/(dx)-sin(x)y