What is the derivative of 7(cos(x^2-2x^2sin(x^2))) ?

The derivative of 7(cos(x^2-2x^2sin(x^2))) is 7(-6xsin(x^2)-4x^3cos(x^2))

What is the first derivative of 7(cos(x^2-2x^2sin(x^2))) ?

The first derivative of 7(cos(x^2-2x^2sin(x^2))) is 7(-6xsin(x^2)-4x^3cos(x^2))

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\frac{d}{d x} (7 (cos (x^{2}) - 2 x^{2} sin (x^{2})))

7 (- 6 x sin (x^{2}) - 4 x^{3} cos (x^{2}))

Solution steps

\frac{d}{d x} (7 (cos (x^{2}) - 2 x^{2} sin (x^{2})))

Take the constant out:

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

= 7 \frac{d}{d x} (cos (x^{2}) - 2 x^{2} sin (x^{2}))

Apply the Sum/Difference Rule:

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

= 7 (\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}))

= 7 (- 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})

= 7 (- 6 x sin (x^{2}) - 4 x^{3} cos (x^{2}))

f (x) = x^{2} 2^{x}

\int \frac{5}{x ^{2} + 4 x - 1} d x

\int \frac{1}{x ( x ^{2} + 1 )} d x

cos (e^{- t^{2}})

\int_{0}^{π} sin (6 x) cos (3 x) d x

What is the derivative of 7(cos(x^2-2x^2sin(x^2))) ?
The derivative of 7(cos(x^2-2x^2sin(x^2))) is 7(-6xsin(x^2)-4x^3cos(x^2))
What is the first derivative of 7(cos(x^2-2x^2sin(x^2))) ?
The first derivative of 7(cos(x^2-2x^2sin(x^2))) is 7(-6xsin(x^2)-4x^3cos(x^2))