What is the derivative of 6xsin(x^2) ?

The derivative of 6xsin(x^2) is 6(sin(x^2)+2x^2cos(x^2))

What is the first derivative of 6xsin(x^2) ?

The first derivative of 6xsin(x^2) is 6(sin(x^2)+2x^2cos(x^2))

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derivative of

6 x sin (x^{2})

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

Solution steps

\frac{d}{d x} (6 x sin (x^{2}))

Take the constant out:

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

= 6 \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})

= 6 (\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

= 6 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

Simplify

6 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : 6 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= 6 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

y = 1 - x^{2}, y = x^{2} - 1

y^{^{''}} + 3 y^{^{'}} - 12 y = 0

y = \frac{- 13}{3 x}

\int x sin (x^{\frac{3}{2}} + 1) d x

\frac{1}{x + 3}

What is the derivative of 6xsin(x^2) ?
The derivative of 6xsin(x^2) is 6(sin(x^2)+2x^2cos(x^2))
What is the first derivative of 6xsin(x^2) ?
The first derivative of 6xsin(x^2) is 6(sin(x^2)+2x^2cos(x^2))