What is the derivative of 3xsin(x^2) ?

The derivative of 3xsin(x^2) is 3(sin(x^2)+2x^2cos(x^2))

What is the first derivative of 3xsin(x^2) ?

The first derivative of 3xsin(x^2) is 3(sin(x^2)+2x^2cos(x^2))

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\frac{d}{d x} (3 x sin (x^{2}))

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

Solution steps

\frac{d}{d x} (3 x sin (x^{2}))

Take the constant out:

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

= 3 \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})

= 3 (\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

= 3 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

Simplify

3 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : 3 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= 3 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

f (x) = 2 - 3 x

\int - 7 sec^{2} (x) d x

y^{^{'}} + 5 y = 0, y (0) = 2

\int (5 x^{2} - 5 x + 4 tan (x)) d x

What is the derivative of 3xsin(x^2) ?
The derivative of 3xsin(x^2) is 3(sin(x^2)+2x^2cos(x^2))
What is the first derivative of 3xsin(x^2) ?
The first derivative of 3xsin(x^2) is 3(sin(x^2)+2x^2cos(x^2))