What is the derivative of-sin(x^22x) ?

The derivative of-sin(x^22x) is -2(2x^2cos(x^2)+sin(x^2))

What is the first derivative of-sin(x^22x) ?

The first derivative of-sin(x^22x) is -2(2x^2cos(x^2)+sin(x^2))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{d y}{d x} + 9 (tan (9 x)) y = cos (9 x)

x \to 4 - lim (\frac{∣ 2 x ∣}{x})

- 32 t

\frac{d}{d x} (2 cos (x))

f (x) = 7 - 4 x, at x = - 1

What is the derivative of-sin(x^22x) ?
The derivative of-sin(x^22x) is -2(2x^2cos(x^2)+sin(x^2))
What is the first derivative of-sin(x^22x) ?
The first derivative of-sin(x^22x) is -2(2x^2cos(x^2)+sin(x^2))