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

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

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

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

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derivative of

- 4 x sin (2 x^{2})

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

f (x) = - 8 (4 x + 3)^{- 3}, at x = 3

\frac{d}{d x} (cot (x) + csc (x))

x \to 1 lim (\frac{1 - x ^{2}}{ln ( x )})

y^{^{'}} + \frac{4 y}{x} = - \frac{3}{x}

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