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

The derivative of 2sin(2+3x^2) is 12xcos(2+3x^2)

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

The first derivative of 2sin(2+3x^2) is 12xcos(2+3x^2)

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derivative of

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

12 x cos (2 + 3 x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 + 3 x^{2}) = 6 x

= 2 cos (2 + 3 x^{2}) \cdot 6 x

Simplify

= 12 x cos (2 + 3 x^{2})

What is the derivative of 2sin(2+3x^2) ?
The derivative of 2sin(2+3x^2) is 12xcos(2+3x^2)
What is the first derivative of 2sin(2+3x^2) ?
The first derivative of 2sin(2+3x^2) is 12xcos(2+3x^2)