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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

\frac{d x}{d x} = 1

= 2 ((- sin (x^{2}) \cdot 2 x) x + 1 \cdot cos (x^{2}))

Simplify

2 ((- sin (x^{2}) \cdot 2 x) x + 1 \cdot cos (x^{2})) : 2 (- 2 x^{2} sin (x^{2}) + cos (x^{2}))

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

\frac{\partial}{\partial x} (x e^{y} - 1)

x^{2} + y^{2} = 27

\int_{1}^{x} \frac{e ^{- 3 t}}{t} d t

3 x^{2}, (5, 75)

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

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