What is the derivative of cos(2xy) ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = cos (2 x), g = y

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

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

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

Simplify

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

y = x^{2} - 6, y = 3

y = e^{3 x}, y = e^{x}, [0, 2]

\frac{d}{d x} (\frac{24}{x ^{5}})

\int x^{7} e^{x} d x

y^{^{'}} - \frac{3}{x} y = x^{2}

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