What is the derivative of 2xcos(x^2) ?

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

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

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

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derivative of

2 x cos (x^{2})

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

x + 3 3 x^{2} - 2 x + 5

- y^{2} - y e^{t} + (y + e^{t}) (\frac{d y}{d t}) = 0

\int \frac{1}{( 6 x ^{2} + 9 ) ^{4}} x d x

x \to \infty lim (1 + \frac{6}{x})

\int_{0}^{\frac{π}{6}} sin (2 x) d x

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