What is the derivative of 2cos(2+x^3) ?

The derivative of 2cos(2+x^3) is -6x^2sin(2+x^3)

What is the first derivative of 2cos(2+x^3) ?

The first derivative of 2cos(2+x^3) is -6x^2sin(2+x^3)

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derivative of

2 cos (2 + x^{3})

- 6 x^{2} sin (2 + x^{3})

Solution steps

\frac{d}{d x} (2 cos (2 + x^{3}))

Take the constant out:

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

= 2 \frac{d}{d x} (cos (2 + x^{3}))

Apply the chain rule:

- sin (2 + x^{3}) \frac{d}{d x} (2 + x^{3})

= - sin (2 + x^{3}) \frac{d}{d x} (2 + x^{3})

\frac{d}{d x} (2 + x^{3}) = 3 x^{2}

= 2 (- sin (2 + x^{3}) \cdot 3 x^{2})

Simplify

= - 6 x^{2} sin (2 + x^{3})

What is the derivative of 2cos(2+x^3) ?
The derivative of 2cos(2+x^3) is -6x^2sin(2+x^3)
What is the first derivative of 2cos(2+x^3) ?
The first derivative of 2cos(2+x^3) is -6x^2sin(2+x^3)