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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{\partial}{\partial x} (3 ln (x))

(x + 6), x, - 2, 3

\int sec^{6} (x) tan (x) d x

y = 2 3^{x}

y = ln (7 x)

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