What is the derivative of-2sin(x^2-4x^2cos(x^2)) ?

The derivative of-2sin(x^2-4x^2cos(x^2)) is -12xcos(x^2)+8x^3sin(x^2)

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

The first derivative of-2sin(x^2-4x^2cos(x^2)) is -12xcos(x^2)+8x^3sin(x^2)

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\frac{d}{d x} (- 2 sin (x^{2}) - 4 x^{2} cos (x^{2}))

- 12 x cos (x^{2}) + 8 x^{3} sin (x^{2})

Solution steps

\frac{d}{d x} (- 2 sin (x^{2}) - 4 x^{2} cos (x^{2}))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (2 sin (x^{2})) - \frac{d}{d x} (4 x^{2} cos (x^{2}))

\frac{d}{d x} (2 sin (x^{2})) = 4 x cos (x^{2})

\frac{d}{d x} (4 x^{2} cos (x^{2})) = 4 (2 x cos (x^{2}) - 2 x^{3} sin (x^{2}))

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

Simplify

- 4 x cos (x^{2}) - 4 (2 x cos (x^{2}) - 2 x^{3} sin (x^{2})) : - 12 x cos (x^{2}) + 8 x^{3} sin (x^{2})

= - 12 x cos (x^{2}) + 8 x^{3} sin (x^{2})

\int \frac{1}{x ^{2} + x - 12} d x

t e^{- t}

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - 1}{- 2 x ^{7}})

\frac{d}{d x} (x^{3} + 2 x^{2} + x - 7)

\frac{d}{d θ} (- cos (θ))

What is the derivative of-2sin(x^2-4x^2cos(x^2)) ?
The derivative of-2sin(x^2-4x^2cos(x^2)) is -12xcos(x^2)+8x^3sin(x^2)
What is the first derivative of-2sin(x^2-4x^2cos(x^2)) ?
The first derivative of-2sin(x^2-4x^2cos(x^2)) is -12xcos(x^2)+8x^3sin(x^2)