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

The derivative of 2cos(x^2sin(2x)) is 2(-2xsin(x^2)sin(2x)+2cos(2x)cos(x^2))

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

The first derivative of 2cos(x^2sin(2x)) is 2(-2xsin(x^2)sin(2x)+2cos(2x)cos(x^2))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x^{2}), g = sin (2 x)

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

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

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

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

Simplify

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

\frac{1}{s}

\frac{5 s + 5}{s ^{3} + 6 s ^{2} + 10 s}

\frac{\partial}{\partial x} (x^{2} - 6 x y + y)

(- 4, - 3), (4, 2)

\int_{0}^{2} 6 x - x^{2} d x

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