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

The derivative of 4cos(4x^2) is -32xsin(4x^2)

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

The first derivative of 4cos(4x^2) is -32xsin(4x^2)

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derivative of

4 cos (4 x^{2})

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

- sin (4 x^{2}) \frac{d}{d x} (4 x^{2})

= - sin (4 x^{2}) \frac{d}{d x} (4 x^{2})

\frac{d}{d x} (4 x^{2}) = 8 x

= 4 (- sin (4 x^{2}) \cdot 8 x)

Simplify

= - 32 x sin (4 x^{2})

What is the derivative of 4cos(4x^2) ?
The derivative of 4cos(4x^2) is -32xsin(4x^2)
What is the first derivative of 4cos(4x^2) ?
The first derivative of 4cos(4x^2) is -32xsin(4x^2)