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Popular >

derivative of cos(xcos(y))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral from 1 to 4 of (x^2+2)/(5x-x^2)

\int_{1}^{4} \frac{x ^{2} + 2}{5 x - x ^{2}} d x

tangent of sqrt(x)(25.5)tangent of

x (25.5)

derivative of x^2-4x-2

\frac{d}{d x} (x^{2} - 4 x - 2)

tangent of f(x)=(4x)/(x+2),(2,2)tangent of

f (x) = \frac{4 x}{x + 2}, (2, 2)

(\partial)/(\partial x)((2x+2)/(y^3))

\frac{\partial}{\partial x} (\frac{2 x + 2}{y ^{3}})

Frequently Asked Questions (FAQ)

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