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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = sin (x), g = cos (y)

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

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

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

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

Simplify

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

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