What is the derivative of sin(xx) ?

The derivative of sin(xx) is xcos(x)+sin(x)

What is the first derivative of sin(xx) ?

The first derivative of sin(xx) is xcos(x)+sin(x)

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

x cos (x) + sin (x)

Solution steps

\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

= \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

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

Simplify

= x cos (x) + sin (x)

sin (a x)

\int \frac{1}{16 x ^{2} - 9} d x

\frac{\partial}{\partial x} (x y sin (y))

\int \frac{( ln ( x ) + 2 ) ^{2}}{2} d x

\int \frac{e ^{x}}{e ^{x} - 5} d x

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