What is the derivative of 2xcos(y) ?

The derivative of 2xcos(y) is 2(cos(y)-xsin(y)(dy)/(dx))

What is the first derivative of 2xcos(y) ?

The first derivative of 2xcos(y) is 2(cos(y)-xsin(y)(dy)/(dx))

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = cos (y)

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

\frac{d x}{d x} = 1

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

= 2 (1 \cdot cos (y) + (- sin (y) \frac{d y}{d x}) x)

Simplify

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

\frac{12}{x ^{3}}

\int - 8 d x

15 t^{2}

- 4 csc^{2} (x) + 4 sec^{2} (x)

y = (x^{2} + x + 1)^{100}

What is the derivative of 2xcos(y) ?
The derivative of 2xcos(y) is 2(cos(y)-xsin(y)(dy)/(dx))
What is the first derivative of 2xcos(y) ?
The first derivative of 2xcos(y) is 2(cos(y)-xsin(y)(dy)/(dx))