What is the derivative of 3(cos(x^2)-2x^2sin(x^2)) ?

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

What is the first derivative of 3(cos(x^2)-2x^2sin(x^2)) ?

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Expand

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

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

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

y = ln (lo g_{e} (3 x))

- 4

\int_{1}^{\infty} 0 d x

\int sec (x) tan^{4} (x) d x

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