What is the derivative of 4xsin(x^2) ?

The derivative of 4xsin(x^2) is 4(sin(x^2)+2x^2cos(x^2))

What is the first derivative of 4xsin(x^2) ?

The first derivative of 4xsin(x^2) is 4(sin(x^2)+2x^2cos(x^2))

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\frac{d}{d x} (4 x sin (x^{2}))

4 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

Solution steps

\frac{d}{d x} (4 x sin (x^{2}))

Take the constant out:

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

= 4 \frac{d}{d x} (x sin (x^{2}))

Apply the Product Rule:

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

f = x, g = sin (x^{2})

= 4 (\frac{d x}{d x} sin (x^{2}) + \frac{d}{d x} (sin (x^{2})) x)

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

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

= 4 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

Simplify

4 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : 4 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= 4 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\frac{d}{d x} (\frac{2 - x}{1 - y})

\frac{\partial}{\partial x} (e^{- \frac{x}{2}})

\int \frac{1}{4} sin (4 x) d x

(- 3, 3), (4, - 5)

\frac{9}{x + 1}

What is the derivative of 4xsin(x^2) ?
The derivative of 4xsin(x^2) is 4(sin(x^2)+2x^2cos(x^2))
What is the first derivative of 4xsin(x^2) ?
The first derivative of 4xsin(x^2) is 4(sin(x^2)+2x^2cos(x^2))