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

The derivative of 2(-2x^2sin(x^2+cos(x^2))) is 2(-4x^3cos(x^2)-6xsin(x^2))

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

The first derivative of 2(-2x^2sin(x^2+cos(x^2))) is 2(-4x^3cos(x^2)-6xsin(x^2))

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

2 (- 4 x^{3} cos (x^{2}) - 6 x sin (x^{2}))

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Expand

- 2 (2 x sin (x^{2}) + 2 x^{3} cos (x^{2})) - sin (x^{2}) \cdot 2 x : - 4 x^{3} cos (x^{2}) - 6 x sin (x^{2})

= 2 (- 4 x^{3} cos (x^{2}) - 6 x sin (x^{2}))

\frac{4}{x - 3}

\frac{d ^{2}}{d x ^{2}} (3^{x^{2} - x + 5})

17 y^{^{'}} = y

\int \frac{1}{x 4 x ^{2} + 16} d x

x \to 1 lim (e^{7 x^{3} - 7 x})

What is the derivative of 2(-2x^2sin(x^2+cos(x^2))) ?
The derivative of 2(-2x^2sin(x^2+cos(x^2))) is 2(-4x^3cos(x^2)-6xsin(x^2))
What is the first derivative of 2(-2x^2sin(x^2+cos(x^2))) ?
The first derivative of 2(-2x^2sin(x^2+cos(x^2))) is 2(-4x^3cos(x^2)-6xsin(x^2))