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

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

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

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

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derivative of

2 x sin (x^{2})

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

Solution steps

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

Take the constant out:

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

= 2 \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})

= 2 (\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

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

Simplify

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

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

\frac{d}{d x} (\frac{b a ^{2} - x ^{2}}{a})

x \to 3 lim (2 x + 5)

\frac{d}{d x} (\frac{4}{x ^{11}})

(y + x cot (\frac{y}{x})) d x - x d y = 0

x \to \infty lim (x \cdot 2^{x})

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