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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

= 4 (\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}))

= 4 (- 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})

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

\int tan^{3} (x) sec^{4} (x) d x

\int x^{- 5} d x

\int \frac{2 x + 1}{x ^{2} + 6 x + 10} d x

t \to \infty lim (\frac{1}{4 t})

f (x) = \frac{x}{x + 6}

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