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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Expand

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

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

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

f (x) = 4 + x - 2 x^{2} - 3 x^{3}, at x = 2

x \to 1 lim (\frac{2}{x ^{3} - 1})

\frac{d}{d x} (sin (x^{c o s (x)}))

y^{^{'}} = 3 + e^{- 2 t}

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