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

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

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

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

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

- 4 x sin (x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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