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

The derivative of (sin(x)dx) is d(xcos(x)+sin(x))

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

The first derivative of (sin(x)dx) is d(xcos(x)+sin(x))

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

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

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = sin (x), g = x

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

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

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

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

Simplify

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

x \to 2 lim (\frac{x - 1}{x - 2})

x \to 0 + lim (cos^{\frac{1}{x}} (x))

\frac{\partial}{\partial x} (y^{5} - 3 x y)

x^{^{''}} + 4 x^{^{'}} + 4 x = 0

\frac{60 t + 180}{t + 6}

What is the derivative of (sin(x)dx) ?
The derivative of (sin(x)dx) is d(xcos(x)+sin(x))
What is the first derivative of (sin(x)dx) ?
The first derivative of (sin(x)dx) is d(xcos(x)+sin(x))