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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (y)

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

\frac{d x}{d x} = 1

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

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

Simplify

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

x \to 0 lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )})

\int cos (3 t) d t

\frac{d}{d x} (2 f (x))

\int (e^{- x^{2}})^{2} d x

\int \frac{x ^{2}}{3} d x

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