What is the derivative of 2sin(x^2-1) ?

The derivative of 2sin(x^2-1) is 4xcos(x^2-1)

What is the first derivative of 2sin(x^2-1) ?

The first derivative of 2sin(x^2-1) is 4xcos(x^2-1)

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\frac{d}{d x} (2 sin (x^{2} - 1))

4 x cos (x^{2} - 1)

Solution steps

\frac{d}{d x} (2 sin (x^{2} - 1))

Take the constant out:

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

= 2 \frac{d}{d x} (sin (x^{2} - 1))

Apply the chain rule:

cos (x^{2} - 1) \frac{d}{d x} (x^{2} - 1)

= cos (x^{2} - 1) \frac{d}{d x} (x^{2} - 1)

\frac{d}{d x} (x^{2} - 1) = 2 x

= 2 cos (x^{2} - 1) \cdot 2 x

Simplify

= 4 x cos (x^{2} - 1)

What is the derivative of 2sin(x^2-1) ?
The derivative of 2sin(x^2-1) is 4xcos(x^2-1)
What is the first derivative of 2sin(x^2-1) ?
The first derivative of 2sin(x^2-1) is 4xcos(x^2-1)