What is the derivative of cos(x-2xy) ?

The derivative of cos(x-2xy) is -sin(x)-2(y+x(dy)/(dx))

What is the first derivative of cos(x-2xy) ?

The first derivative of cos(x-2xy) is -sin(x)-2(y+x(dy)/(dx))

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\frac{d}{d x} (cos (x) - 2 x y)

- sin (x) - 2 (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (cos (x) - 2 x y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (cos (x)) - \frac{d}{d x} (2 x y)

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

\frac{d}{d x} (2 x y) = 2 (y + x \frac{d y}{d x})

= - sin (x) - 2 (y + x \frac{d y}{d x})

What is the derivative of cos(x-2xy) ?
The derivative of cos(x-2xy) is -sin(x)-2(y+x(dy)/(dx))
What is the first derivative of cos(x-2xy) ?
The first derivative of cos(x-2xy) is -sin(x)-2(y+x(dy)/(dx))