What is the derivative of 6x*sin(3x^2) ?

The derivative of 6x*sin(3x^2) is 6(sin(3x^2)+6x^2cos(3x^2))

What is the first derivative of 6x*sin(3x^2) ?

The first derivative of 6x*sin(3x^2) is 6(sin(3x^2)+6x^2cos(3x^2))

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\frac{d}{d x} (6 x \cdot sin (3 x^{2}))

6 (sin (3 x^{2}) + 6 x^{2} cos (3 x^{2}))

Solution steps

\frac{d}{d x} (6 x sin (3 x^{2}))

Take the constant out:

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

= 6 \frac{d}{d x} (x sin (3 x^{2}))

Apply the Product Rule:

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

f = x, g = sin (3 x^{2})

= 6 (\frac{d x}{d x} sin (3 x^{2}) + \frac{d}{d x} (sin (3 x^{2})) x)

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

\frac{d}{d x} (sin (3 x^{2})) = cos (3 x^{2}) \cdot 6 x

= 6 (1 \cdot sin (3 x^{2}) + cos (3 x^{2}) \cdot 6 xx)

Simplify

6 (1 \cdot sin (3 x^{2}) + cos (3 x^{2}) \cdot 6 xx) : 6 (sin (3 x^{2}) + 6 x^{2} cos (3 x^{2}))

= 6 (sin (3 x^{2}) + 6 x^{2} cos (3 x^{2}))

\frac{d}{d x} (ln (\frac{4 - x}{4 + x}))

\int_{0}^{3} c (3 - x) d x

\int \frac{5 x - 3}{x + 1} d x

f (x) = \frac{4}{3 x ^{2}}

\int \frac{x ^{2} e ^{x}}{( x + 2 ) ^{2}} d x

What is the derivative of 6x*sin(3x^2) ?
The derivative of 6x*sin(3x^2) is 6(sin(3x^2)+6x^2cos(3x^2))
What is the first derivative of 6x*sin(3x^2) ?
The first derivative of 6x*sin(3x^2) is 6(sin(3x^2)+6x^2cos(3x^2))