What is the derivative of 4xcos(x^2) ?

The derivative of 4xcos(x^2) is 4(cos(x^2)-2x^2sin(x^2))

What is the first derivative of 4xcos(x^2) ?

The first derivative of 4xcos(x^2) is 4(cos(x^2)-2x^2sin(x^2))

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derivative of

4 x cos (x^{2})

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

Solution steps

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

Take the constant out:

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

= 4 \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})

= 4 (\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

= 4 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x)

Simplify

4 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x) : 4 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

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

g (x) = \frac{1 - 3 t}{6 + t}

\frac{d y}{d x} + 4 x^{3} y = x^{3}

\int \frac{41}{x ^{3} - 125} d x

\int \frac{ln ( 15 x )}{x} d x

- 4 \cdot arcsin (x)

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