What is the derivative of y=8xsin(x^2) ?

The derivative of y=8xsin(x^2) is 8(sin(x^2)+2x^2cos(x^2))

What is the first derivative of y=8xsin(x^2) ?

The first derivative of y=8xsin(x^2) is 8(sin(x^2)+2x^2cos(x^2))

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derivative of

y = 8 x sin (x^{2})

8 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

Solution steps

\frac{d}{d x} (8 x sin (x^{2}))

Take the constant out:

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

= 8 \frac{d}{d x} (x sin (x^{2}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (x^{2})

= 8 (\frac{d x}{d x} sin (x^{2}) + \frac{d}{d x} (sin (x^{2})) x)

\frac{d x}{d x} = 1

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

= 8 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

Simplify

8 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : 8 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= 8 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

What is the derivative of y=8xsin(x^2) ?
The derivative of y=8xsin(x^2) is 8(sin(x^2)+2x^2cos(x^2))
What is the first derivative of y=8xsin(x^2) ?
The first derivative of y=8xsin(x^2) is 8(sin(x^2)+2x^2cos(x^2))