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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Expand

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

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

f (x) = \frac{1}{3 x}, at x = 9

x \to - 7 lim (\frac{7 - ∣ x ∣}{7 + x})

\int_{1}^{5} \frac{ln ( y )}{x y} d y

(e^{- 4 x})^{^{'}}

\int 30 x^{2} d x

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