What is the derivative of y=12xsin(x) ?

The derivative of y=12xsin(x) is 12(sin(x)+xcos(x))

What is the first derivative of y=12xsin(x) ?

The first derivative of y=12xsin(x) is 12(sin(x)+xcos(x))

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derivative of

y = 12 x sin (x)

12 (sin (x) + x cos (x))

Solution steps

\frac{d}{d x} (12 x sin (x))

Take the constant out:

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

= 12 \frac{d}{d x} (x sin (x))

Apply the Product Rule:

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

f = x, g = sin (x)

= 12 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

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

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

= 12 (1 \cdot sin (x) + cos (x) x)

Simplify

= 12 (sin (x) + x cos (x))

9 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 2 x e^{- y}

t^{4}

\frac{\partial}{\partial x} (ln (\frac{x}{y} + \frac{y}{x}))

\frac{d}{d x} (ln (sin (7 x)))

\frac{d}{d x} (- x^{2} - 2 x + 3)

What is the derivative of y=12xsin(x) ?
The derivative of y=12xsin(x) is 12(sin(x)+xcos(x))
What is the first derivative of y=12xsin(x) ?
The first derivative of y=12xsin(x) is 12(sin(x)+xcos(x))