What is the derivative of 2sin^2(6x^4) ?

The derivative of 2sin^2(6x^4) is 96x^3sin(6x^4)cos(6x^4)

What is the first derivative of 2sin^2(6x^4) ?

The first derivative of 2sin^2(6x^4) is 96x^3sin(6x^4)cos(6x^4)

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derivative of

2 sin^{2} (6 x^{4})

96 x^{3} sin (6 x^{4}) cos (6 x^{4})

Solution steps

\frac{d}{d x} (2 sin^{2} (6 x^{4}))

Take the constant out:

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

= 2 \frac{d}{d x} (sin^{2} (6 x^{4}))

Apply the chain rule:

2 sin (6 x^{4}) \frac{d}{d x} (sin (6 x^{4}))

= 2 sin (6 x^{4}) \frac{d}{d x} (sin (6 x^{4}))

\frac{d}{d x} (sin (6 x^{4})) = cos (6 x^{4}) \cdot 24 x^{3}

= 2 \cdot 2 sin (6 x^{4}) cos (6 x^{4}) \cdot 24 x^{3}

Simplify

= 96 x^{3} sin (6 x^{4}) cos (6 x^{4})

What is the derivative of 2sin^2(6x^4) ?
The derivative of 2sin^2(6x^4) is 96x^3sin(6x^4)cos(6x^4)
What is the first derivative of 2sin^2(6x^4) ?
The first derivative of 2sin^2(6x^4) is 96x^3sin(6x^4)cos(6x^4)