What is the derivative of (cos(x)dx) ?

The derivative of (cos(x)dx) is d(-xsin(x)+cos(x))

What is the first derivative of (cos(x)dx) ?

The first derivative of (cos(x)dx) is d(-xsin(x)+cos(x))

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

d (- x sin (x) + cos (x))

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = cos (x), g = x

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

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

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

= d ((- sin (x)) x + 1 \cdot cos (x))

Simplify

= d (- x sin (x) + cos (x))

ln (x + 3)

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

\frac{d}{d x} (sin (\frac{x ^{2} - 1}{x}))

\frac{\partial}{\partial x} (e^{2 x} cos (6 y))

\frac{d}{d x} (sin^{3} (cos (x)))

What is the derivative of (cos(x)dx) ?
The derivative of (cos(x)dx) is d(-xsin(x)+cos(x))
What is the first derivative of (cos(x)dx) ?
The first derivative of (cos(x)dx) is d(-xsin(x)+cos(x))