What is the derivative of cos(xsin(y)) ?

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

What is the first derivative of cos(xsin(y)) ?

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

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\frac{d}{d x} (cos (x) 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{1}{x ^{2}}, 4

y^{^{'}} = y (x y^{6} + 5)

\int_{1}^{9} 2^{x} d x

\int \frac{2}{( x + 2 ) ^{2}} d x

\frac{d}{d x} (3 x^{4} + 4 x^{3})

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