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

The derivative of 4sin(x^2) is 8xcos(x^2)

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

The first derivative of 4sin(x^2) is 8xcos(x^2)

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

8 x cos (x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 4 cos (x^{2}) \cdot 2 x

Simplify

= 8 x cos (x^{2})

What is the derivative of 4sin(x^2) ?
The derivative of 4sin(x^2) is 8xcos(x^2)
What is the first derivative of 4sin(x^2) ?
The first derivative of 4sin(x^2) is 8xcos(x^2)